0. Review of Algebra

Factoring Polynomials

0. Review of Algebra

Factoring Polynomials

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07:30

Introduction to Factoring Polynomials

Factor Using Special Product Formulas

Factor Using the AC Method When a Is 1

Factor Using the AC Method When a Is Not 1

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06:17

Whiteboard Math: Factoring by Grouping

How to factor a perfect square trinomial

Factoring Sum and Difference of Cubes

Mario's Math Tutoring

Lesson: Factoring a Sum or Difference of Cubes

Factoring a sum or difference of two cubes

KSpinMATH

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Practice this topic

Multiple Choice

Factor out the Greatest Common Factor in the polynomial.

$4x^2y-100y$

Factor out the Greatest Common Factor in the polynomial.

$-3x^4+12x^3-18x^2$

Factor the polynomial by grouping

$-x^2-5x+7x+35$

Factor the polynomial by grouping.

$6x^3-2x^2+3x-1$

Factor the polynomial using special product formulas.

$25x^2-110x+121$

Factor the polynomial using special product formulas.

$\frac{x^2}{49}-9$

Factor the polynomial.

$x^2-13x+40$

Factor the polynomial.

$x^2-2x-15$

Factor the polynomial.

$4x^2-19x+12$

Factor the polynomial.

$3x^2-2x-5$

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. x² - 4

232

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Textbook Question

In Exercises 1–10, factor out the greatest common factor. 18x+27

369

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x³ − 16x

230

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Textbook Question

In Exercises 1–10, factor out the greatest common factor. 3x^2+6x

357

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + 8x + 12

274

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Textbook Question

In Exercises 1–10, factor out the greatest common factor. 9x^4−18x^3+27x^2

509

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + 9x + 20

229

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. x³ + 5x²

246

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Textbook Question

Work each problem. Match each polynomial in Column I with its factored form in Column II. a. x^2 + 10xy +25y^2 b. x^2-10xy +25y^2 c.x^2-25y^2 d. 25y^2-x^2 A. (x+5y ) (x-5y) B. (x+5y)^2 C. (x-5y)^2 D. (5y+x)(5y-x)

431

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x²y − 16y + 32 − 2x²

231

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. y² + 10y + 16

214

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 12x⁴ − 8x²

322

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. 36x² - 49y²

255

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 4a²b − 2ab − 30b

242

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − 8x + 15

218

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 32x⁴ + 2x³ + 8x²

222

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. x²y² - 1

242

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Textbook Question

Work each problem. Which of the following is the correct complete factorization of x^4-1? A. (x^2-1)(x^2+1) B.(x^2+1)(x+1)(x-1) C. (x^2-1)^2 D. (x-1)^2(x+1)^2

360

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Textbook Question

Work each problem. Which of the following is the correct factorization of x^3+8? A. (x+2)^3 B. (x+2)(x^2+2x+4) C. (x+2)(x^2-2x+4) D. (x+2)(x^2-4x+4)

351

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. y² − 12y + 20

227

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 4x²y³ + 6xy

205

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. 9x⁴ - 25y⁶

217

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 12m+60

605

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Textbook Question

Express the distance between the numbers -17 and 4 using absolute value. Then evaluate the absolute value.

426

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Textbook Question

In Exercises 11–16, factor by grouping. x^3−3x^2+4x−12

378

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. a² + 5a − 14

244

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 30x²y³ − 10xy²

275

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. x¹⁴ - y⁴

210

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 8k^3+24k

388

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 11x⁵ − 11xy²

234

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Textbook Question

In Exercises 11–16, factor by grouping. x^3+6x^2−2x−12

300

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + x − 30

216

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 12xy − 6xz + 4xw

218

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. (x - 3)² - y²

230

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. xy-5xy^2

450

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 4x⁵ − 64x

246

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 5h^2j+hj

306

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Textbook Question

In Exercises 16–17, factor completely. xy − 6x + 2y − 12

225

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. -4p^3q^4-2p^2q^5

508

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Textbook Question

In Exercises 1–22, factor each difference of two squares. Assume that any variable exponents represent whole numbers. a² - (b - 2)²

223

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x³ − 4x² − 9x + 36

224

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Textbook Question

In Exercises 16–17, factor completely. 24x³y + 16x²y − 30xy

252

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Textbook Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. x^2+8x+15

431

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 2x⁵ + 54x²

230

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Textbook Question

Simplify the algebraic expression. 5(2x - 3) + 7x

Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)

425

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − x + 7

203

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Textbook Question

In Exercises 1–22, factor the greatest common factor from each polynomial. 15x²ⁿ − 25xⁿ

207

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 2(a+b)+4m(a+b)

529

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Textbook Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. x^2−14x+45

389

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 6x(a+b)-4y(a+b)

459

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Textbook Question

In Exercises 23–48, factor completely, or state that the polynomial is prime. 2x³ - 8x

203

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. (5r-6)(r+3)-(2r-1)(r+3)

578

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − 9xy + 14y²

205

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −4x + 12

236

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. (4z-5)(3z-2)-(3z-9)(3z-2)

989

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Textbook Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 2x^2+5x−3

349

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Textbook Question

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. 24. x² + 4x

231

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)^2+2(m-1)^3

481

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Textbook Question

In Exercises 23–48, factor completely, or state that the polynomial is prime. 50 - 2y²

236

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − xy − 30y²

224

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −8x − 48

220

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²

265

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Textbook Question

Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)^3-2(a+3)+(a+3)^2

320

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Textbook Question

In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 6x^2−11x+4

323

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Textbook Question

In Exercises 23–48, factor completely, or state that the polynomial is prime. 8x² - 8y²

206

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + xy + y²

217

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −2x² + 6x − 14

221

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Textbook Question

Concept Check When directed to completely factor the polynomial 4x^2y^5-8xy^3,a student wrote 2xy^3(2xy^2-4). When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.

347

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 4x² + 25y²

225

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − xy + y²

221

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Textbook Question

Concept Check Kurt factored 16a^2-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?

361

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −5y² + 40x

228

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 12x³y − 12xy³

227

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Textbook Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. a² − 18ab + 45b²

218

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Textbook Question

Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21

371

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Textbook Question

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. 30. x² - 1/3x

263

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −4x³ + 32x² − 20x

243

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. 6bx² + 6by²

229

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Textbook Question

Factor each polynomial by grouping. See Example 2. 4x^6+36-x^6y-9y

407

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Textbook Question

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. 32. x²+4/5x

246

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Textbook Question

In Exercises 23–34, factor out the negative of the greatest common factor. −x² − 7x + 5

195

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x⁴ − xy³ + x³y − y⁴

214

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Textbook Question

Factor each polynomial by grouping. See Example 2. 20z^2-8x+5pz^2-2px

435

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Textbook Question

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. 34. x²-9/5x

245

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Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 4a² + 12x + 36

244

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Textbook Question

In Exercises 23–48, factor completely, or state that the polynomial is prime. 8x² + 8y²

247

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Textbook Question

Factor each trinomial, if possible. See Examples 3 and 4. 8h^2-2h-21

391

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Textbook Question

In Exercises 31–38, factor completely. 4y³ + 12y² − 72y

225

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Textbook Question

In Exercises 23–48, factor completely, or state that the polynomial is prime. x² + 25y²

230

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Showing 100 of 100 practice