4. Polynomial Functions

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^3+5x^2+7x+2)÷(x+2)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (6x^3+7x^2+12x−5)÷(3x−1)

Use synthetic division to perform each division. (x^3 + 3x^2 +11x + 9) / x+1

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x^2−2x+5)/(x−3)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (4x^4−4x^2+6x)/(x−4)

Use synthetic division to perform each division. (3x^3+6x^2-8x+3)/(x+3)

Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x)=(x-k)q(x)+r. ƒ(x)=5x^3-3x^2+2x-6; k=2

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^4+2x^3−4x^2−5x−6)/(x^2+x−2)

Use synthetic division to perform each division. (-9x^3 + 8x^2 - 7x+2) / x-2

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (2x^5+9x^3+3x^2)/(3x^2+1)

Use synthetic division to perform each division. (1/3x^3 - 2/9x^2 + 2/27x - 1/81) / x - 1/3

In Exercises 17–32, divide using synthetic division. (4x^3−3x^2+3x−1)÷(x−1)

In Exercises 17–32, divide using synthetic division. (6x^5−2x^3+4x^2−3x+1)÷(x−2)

Use synthetic division to perform each division. x^7+1 / x+1

Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x-k) q(x) + r. ƒ(x) = 2x^3 + 3x^2 - 16x+10; k = -4

In Exercises 17–32, divide using synthetic division. (x^5+x^3−2)/(x−1)

In Exercises 17–32, divide using synthetic division. (x^7+x^5−10x^3+12)/(x+2)

In Exercises 27–29, divide using long division. (4x^4 +6x^3 + 3x - 1) ÷ (2x^2 + 1)

Given f(x) = 2x^3 - 7x^2 + 9x - 3, use the Remainder Theorem to find f(- 13).

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = - x^3 + 8x^2 + 63; k=4

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x^4+5x^3+5x^2−5x−6;f(3)

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x^4−5x^3−x^2+3x+2;f(− 1/2)

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^4+10x^3+5x^2+x+1;f(− 2/3)

Use synthetic division to divide f(x)=x^3−4x^2+x+6 by x+1. Use the result to find all zeros of f.

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x^5 - 10x^3 - 19x^2 - 50; k=3

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^2 +2x -8; k=2

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^3 + 3x^2 -x + 1; k = 1+i

Find k so that 4x+3 is a factor of 20x^3+23x^2-10x+k.

When 2x^2−7x+9 is divided by a polynomial, the quotient is 2x-3 and the remainder is 3. Find the polynomial.

Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)

Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5m^3)

Perform each division. See Examples 7 and 8. (8wxy^2+3wx^2y+12w^2xy)/(4wx^2y)

Perform each division. See Examples 9 and 10. (q^2+4q-32)/(q-4)

Perform each division. See Examples 9 and 10. (x^2+11x+16)/(x+8)

Perform each division. See Examples 9 and 10. (4x^3+9x^2-10x-6)/(4x+1)

Perform each division. See Examples 9 and 10. (10x^3+11x^2-2x+3)/(5x+3)

Perform each division. See Examples 9 and 10. (x^4+5x^2+5x+27)/(x^2+3)

Perform each division. See Examples 9 and 10. (k^4-4k^2+2k+5)/(k^2+1)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^2+8x+15)÷(x+5)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (2x^3+7x^2+9x−20)/(x+3)

Use synthetic division to perform each division. (x^5 + 3x^4 + 2x^3 + 2x^2 + 3x+1) / x+2

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (6x^3+13x^2−11x−15)/(3x^2−x−3)

Use synthetic division to find ƒ(2). ƒ(x)=x^5+4x^2-2x-4

In Exercises 17–32, divide using synthetic division. (3x^2+7x−20)÷(x+5)

Use synthetic division to perform each division. x^4-1 / x-1

In Exercises 17–32, divide using synthetic division. (x^2−5x−5x^3+x^4)÷(5+x)

In Exercises 27–29, divide using long division. (4x^3 - 3x^2 - 2x + 1) ÷ (x + 1)

In Exercises 17–32, divide using synthetic division. (2x^5−3x^4+x^3−x^2+2x−1)/(x+2)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x^2 - 3x-3; k = 2

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x^3−7x^2−2x+5;f(−3)

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^4+10x^3+5x^2+x+1;f(− 2/3)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 + 4; k = 2i

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^3 +7x^2 + 10x; k=0

In Exercises 53–54, write a polynomial that represents the length of each rectangle. Transcription: The area of the rectangle is 0.5x^3 - 0.3x^2 + 0.22x + 0.06 square units and its width is x + 0.2 units

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^2 - 2x + 2; k = 1-i

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = 4x^4 + x^2 + 17x + 3; k= -3/2

The remainder theorem indicates that when a polynomial ƒ(x) is divided by x-k, the remainder is equal to ƒ(k). Consider the polynomial function ƒ(x) = x^3 - 2x^2 - x+2. Use the remainder theorem to find each of the following. Then determine the coor-dinates of the corresponding point on the graph of ƒ(x). ƒ (1)

Use synthetic division to show that 5 is a solution of x^4−4x^3−9x^2+16x+20=0. Then solve the polynomial equation.

Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18mn^2)/(-14m^2n^3)

Perform each division. See Examples 9 and 10. (p^2+2p+20)/(p+6)

Perform each division. See Examples 9 and 10. (3x^3-2x+5)/(x-3)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (12x^2+x−4)÷(3x−2)

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (2x^3+7x^2+9x−20)/(x+3)

Use synthetic division to perform each division. (x^4 + 4x^3 + 2x^2 + 9x+4) / x+4

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^4−81)/(x−3)

Use synthetic division to find ƒ(2). ƒ(x)=5x^4-12x^2+2x-8

In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷(x−2)

Use synthetic division to perform each division. x^3 - 1 / x-1

In Exercises 17–32, divide using synthetic division. (x^5+4x^4−3x^2+2x+3)÷(x−3)

In Exercises 27–29, divide using long division. (4x^3 - 3x^2 - 2x + 1) ÷ (x + 1)

In Exercises 17–32, divide using synthetic division. (x^4−256)/(x−4)

In Exercises 17–32, divide using synthetic division. (2x^5−3x^4+x^3−x^2+2x−1)/(x+2)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 + 5x+6; k = -2

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x^3−11x^2+7x−5;f(4)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 - 5x+1; k = 2+i

Solve the equation 2x3−3x2−11x+6=0 given that -2 is a zero of f(x)=2x^3−3x^2−11x+6.

Solve the equation 12x^3+16x^2−5x−3=0 given that -3/2 is a root.

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = 2x^3 - 6x^2 -9x + 4; k=1

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = 5x^4 + 2x^3 -x+3; k=2/5

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^2 + 3x + 4; k = 2+i

The remainder theorem indicates that when a polynomial ƒ(x) is divided by x-k, the remainder is equal to ƒ(k). Consider the polynomial function ƒ(x) = x^3 - 2x^2 - x+2. Use the remainder theorem to find each of the following. Then determine the coor-dinates of the corresponding point on the graph of ƒ(x). ƒ (-2)

Use synthetic division to show that 5 is a solution of x^4−4x^3−9x^2+16x+20=0. Then solve the polynomial equation.

Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-14x^2)/(-2x^2)

Perform each division. See Examples 7 and 8. (-4m^2n^2-21mn^3+18mn^2)/(-14m^2n^3)

Perform each division. See Examples 9 and 10. (3t^2+17t+10)/(3t+2)

Perform each division. See Examples 9 and 10. (p^2+2p+20)/(p+6)

Perform each division. See Examples 9 and 10. (4x^3-3x^2+1)/(x-2)

Perform each division. See Examples 9 and 10. (3x^3-2x+5)/(x-3)

Divide 737 by 21 without using a calculator. Write the answer as quotient + remainder/divisor

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (12x^2+x−4)÷(3x−2)

Use synthetic division to perform each division. (5x^4 +5x^3 + 2x^2 - x-3) / x+1

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (x^4−81)/(x−3)

Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x)=(x-k)q(x)+r. ƒ(x)=-3x^3+5x-6; k=-1

Use synthetic division to find ƒ(2). ƒ(x)=2x^3-3x^2+7x-12

In Exercises 17–32, divide using synthetic division. (2x^2+x−10)÷(x−2)

Use synthetic division to perform each division. (x^4 - 3x^3 - 4x^2 + 12x) / x-2

In Exercises 17–32, divide using synthetic division. (x^5+4x^4−3x^2+2x+3)÷(x−3)

In Exercises 17–32, divide using synthetic division. (x^4−256)/(x−4)

Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x-k) q(x) + r. ƒ(x) = 3x^4 + 4x^3 - 10x^2 + 15; k = -1

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x^3−11x^2+7x−5;f(4)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^3 - 4x^2 + 2x+1; k = -1

Use synthetic division to divide f(x)=x^3−4x^2+x+6 by x+1. Use the result to find all zeros of f.

Solve the equation 12x^3+16x^2−5x−3=0 given that -3/2 is a root.

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 6x^4 + x^3 - 8x^2 + 5x+6; k=1/2

Use synthetic division to determine whether the given number k is a zero of the polyno-mial function. If it is not, give the value of ƒ(k). ƒ(x) = x^3 - 3x^2 + 4x -4; k=2

Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5m^3)

Perform each division. See Examples 9 and 10. (q^2+4q-32)/(q-4)

Perform each division. See Examples 9 and 10. (4x^3+9x^2-10x-6)/(4x+1)

Perform each division. See Examples 9 and 10. (x^4+5x^2+5x+27)/(x^2+3)