0. Review of Algebra

Polynomials Intro

0. Review of Algebra

Polynomials Intro

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05:13

Introduction to Polynomials

Standard Form of Polynomials

Adding and Subtracting Polynomials

Practice this topic

Multiple Choice

Perform the indicated operation.

$\left(x^3+3x^2-7x\right)+2\left(x^3-5x^2+9x+4\right)$

Perform the indicated operation.

$\left(-2x^4+10x^3+6x-3\right)-\left(x^4-7x^2+8x+5\right)$

Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4

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Textbook Question

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. 7/(x−3)

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Textbook Question

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x^2−25)

In Exercises 1–8, multiply the monomials. (3x²y⁴)(5xy⁷)

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Textbook Question

In Exercises 1–8, multiply the monomials. (−3xy²z⁵)(2xy⁷z⁴)

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Textbook Question

In Exercises 5–8, find the degree of the polynomial. 3x^2−5x+4

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Textbook Question

Perform the indicated operations. (2x^2-x)+(x^2+4x)

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Textbook Question

In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x^2−6x+9)

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Textbook Question

Perform the indicated operations. -2x^3(x^4-8)

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Textbook Question

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)

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Textbook Question

Perform the indicated operations. (10m^4-4m^2)/2m

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Textbook Question

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (17x^3−5x^2+4x−3)−(5x^3−9x^2−8x+11)

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Textbook Question

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (y^2+7y−18)/(y^2−3y+2)

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. 4xy(7x+3y)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (6x+9)/(3x−15) ⋅ (x−5)/(4x+6)

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. 3ab² (6a²b³+5ab)

220

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Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 15a^2b^3+12a^3b^8-13b^5+12b^6

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Textbook Question

In Exercises 15–58, find each product. (2x−3)(x^2−3x+5)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2−4x+4) ⋅ (2x−4)/(x+2)

In Exercises 15–58, find each product. (x+7)(x+3)

In Exercises 15–58, find each product. (x−1)(x+2)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x+5)/7 ÷ (4x+20)/9

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Textbook Question

In Exercises 15–58, find each product. (2x−5)(7x+2)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x−2) ÷ (x+2)/(4x−8)

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Textbook Question

Add or subtract, as indicated. See Example 2. 3(8p^2-5p) - 5(3p^2-2p+4)

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Textbook Question

In Exercises 23–34, find each product using either a horizontal or a vertical format. (a−b)(a²+ab+b²)

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Textbook Question

Add or subtract, as indicated. See Example 2. -(8x^3+x-3) + (2x^3+x^2) - (4x^2+3x-1)

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Textbook Question

In Exercises 23–34, find each product using either a horizontal or a vertical format. (x²+2x−1)(x²+3x−4)

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Textbook Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (−6x³ + 5x² − 8x + 9) + (17x³ + 2x² − 4x − 13)

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Textbook Question

Find each product. See Examples 3–5. (14r-1)(17r+2)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2+3x−10) ÷ (x^2+5x+6)/(x^2+8x+15)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^3−25x)/4x^2 ⋅ (2x^2−2)/(x^2−6x+5) ÷ (x^2+5x)/(7x+7)

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Textbook Question

In Exercises 15–58, find each product. (x+5)(x−5)

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Textbook Question

Find each product. See Examples 3–5. 2b^3(b^2-4b+3)

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Textbook Question

Find each product. See Examples 3–5. (2z-1)(-z^2+3z-4)

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Textbook Question

In Exercises 15–58, find each product. (5−7x)(5+7x)

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Textbook Question

Find each product. See Examples 3–5. (3w+2)(-w^2+4w-3)

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Textbook Question

In Exercises 15–58, find each product. (4x^2+5x)(4x^2−5x)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. (4x−10)/(x−2) − (x−4)/(x−2)

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Textbook Question

In Exercises 15–58, find each product. (1−y^5)(1+y^5)

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Textbook Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (x²ⁿ + 5xⁿ − 8) + (4x²ⁿ − 7xⁿ + 2)

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Textbook Question

Find each product. See Examples 3–5. (3y-5)(3y+5)(9y^2-25)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (4x+3)(5x+1)

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Textbook Question

Find each product. See Examples 3–5. (x+1)(x+1)(x-1)(x-1)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (3y−4)(2y−1)

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Textbook Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (17x³ − 5x² + 4x − 3) − (5x³ − 9x² − 8x + 11)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 5/x + 3

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Textbook Question

In Exercises 42–46, simplify each algebraic expression. 5x+7x²-4x+2x²

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Textbook Question

Find each product. See Examples 5 and 6. (2m+3)(2m-3)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 2/5x − (x+1)/4x

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Textbook Question

In Exercises 15–58, find each product. (4x^2−1)^2

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Textbook Question

Find each product. See Examples 5 and 6. (a-6b)^2

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (3xy−1)(5xy+2)

213

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Textbook Question

Find each product. See Examples 5 and 6. (5r-3t^2)^2

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (x−4)(x²−5)

216

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Textbook Question

In Exercises 33–68, add or subtract as indicated. (x+9)/10x^3 + 11/15x^2

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Textbook Question

Find each product. See Examples 5 and 6. (2z^4-3y)^2

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Textbook Question

In Exercises 15–58, find each product. (9−5x)^2

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Textbook Question

In Exercises 15–58, find each product. (x+2)^3

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Textbook Question

Subtract −4x³ − x²y + xy² + 3y³ from x³ + 2x²y − y³.

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Textbook Question

Add 6x⁴−5x³+2x to the difference between 4x³+3x²−1 and x⁴−2x²+7x−3.

329

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Textbook Question

Find each product. See Examples 5 and 6. [(3a+b)-1]^2

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Textbook Question

Find each product. See Examples 5 and 6. [(2m+7)-n]^2

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Textbook Question

In Exercises 15–58, find each product. (x−1)^3

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)

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Textbook Question

Find each product. See Examples 5 and 6. (y+2)^3

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (2x + y)²

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (5x − 3y)²

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Textbook Question

Perform the indicated operations. See Examples 2–6. (x^4-3x^2+2) - (-2x^4+x^2-3)

Perform the indicated operations. See Examples 2–6. (7m+2n)^2

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Textbook Question

Perform the indicated operations. See Examples 2–6. (3p+5)^2

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Textbook Question

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x^4 y^2+5x^3 y−3y)−(2x^4 y^2−3x^3 y−4y+6x)

349

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Textbook Question

In Exercises 33–68, add or subtract as indicated. (4x^2+x−6)/(x^2+3x+2)−3x/(x+1)+5/(x+2)

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Textbook Question

In Exercises 67–82, find each product. (3x−y)(2x+5y)

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Textbook Question

Perform the indicated operations. See Examples 2–6. -z^3(9-z) + 4z(2+3z)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 5)(x − 5)

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Textbook Question

Find each product. Assume all variables represent positive real numbers. y^5/8(y^3/8-10y^11/8)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (5x + 3)(5x − 3)

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Textbook Question

Find each product. Assume all variables represent positive real numbers. -4k(k^7/3-6k^1/3)

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Textbook Question

In Exercises 67–82, find each product. (9x+7y)^2

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Textbook Question

In Exercises 67–82, find each product. (x−y)(x^2+xy+y^2)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (1 − y⁵)(1 + y⁵)

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Textbook Question

Find each product : (4x+5)(4x-5)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (2 − y⁵)(2 + y⁵)

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Textbook Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^2-8xy+y^2)+(-8x^2-9xy-4y^2)

Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x^3y^2-5x^2y-9x^2)-(-11x^3y^2-6x^2y+3x^2-4)

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Textbook Question

In Exercises 83–90, perform the indicated operation or operations. (3x+4y)^2−(3x−4y)^2

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Textbook Question

Find each product. (x+7y)(3x-5y)

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Textbook Question

In Exercises 83–90, perform the indicated operation or operations. (3x+5)(2x−9)−(7x−2)(x−1)

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Textbook Question

In Exercises 83–94, find each product. (5x + 7y − 2)(5x + 7y + 2)

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Textbook Question

In Exercises 83–94, find each product. [5y + (2x+3)][5y − (2x+3)]

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Textbook Question

The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. 102^2

In Exercises 117–130, simplify each algebraic expression. 7x+5x

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Textbook Question

In Exercises 117–130, simplify each algebraic expression. 6x²-x²

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