4. Polynomial Functions

Divide using synthetic division. (x⁵+x³−2)/(x−1)

Divide using synthetic division. (x⁷+x⁵−10x³+12)/(x+2)

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

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = - x³ + 8x² + 63; k=4

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x⁴+5x³+5x²−5x−6;f(3)

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x⁴−5x³−x²+3x+2; f(−1/2)

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x⁴+10x³+5x²+x+1; f(−2/3)

Use synthetic division to divide f(x)=x³−4x²+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) = 2x⁵ - 10x³ - 19x² - 50; k=3

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x² +2x -8; k=2

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = x³ + 3x² -x + 1; k = 1+i

When 2x²−7x+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)