4. Polynomial Functions

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)

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)