4. Polynomial Functions

Use synthetic division to perform each division. x⁴-1 / x-1

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $\(\frac{2x^3 + 7x^2 + 9x - 20}{x + 3}\)$

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

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

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) = 2x³ + 3x² - 16x+10; k = -4

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x³−7x²−2x+5;f(−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) = x³ +7x² + 10x; k=0

Use synthetic division to divide f(x)=x³−4x²+x+6 by x+1. Use the result to find all zeros of f.

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)=5x³-3x²+2x-6; 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 + 4x -4; k=2

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 6x⁴ + x³ - 8x² + 5x+6; k=1/2

Use synthetic division to find ƒ(2). ƒ(x)=x⁵+4x²-2x-4

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

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) = 5x⁴ + 2x³ -x+3; k=2/5