4. Polynomial Functions

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(12x^2+x-4)÷(3x-2)$

Use synthetic division to perform each division. (x⁴ + 4x³ + 2x² + 9x+4) / x+4

Divide using long division. State the quotient, and the remainder, r(x). (x⁴−81)/(x−3)

Use synthetic division to find ƒ(2). ƒ(x)=5x⁴-12x²+2x-8

Divide using synthetic division. (2x²+x−10)÷(x−2)

Use synthetic division to perform each division. (x³ - 1) / (x-1)

Divide using synthetic division. (x⁵+4x⁴−3x²+2x+3)÷(x−3)

Divide using synthetic division. (x⁴−256)/(x−4)

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

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x³−11x²+7x−5;f(4)

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

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

Solve the equation 12x³+16x²−5x−3=0 given that -3/2 is a root.

Use synthetic division to determine whether the given number k is a zero of the polynomial function. If it is not, give the value of ƒ(k). ƒ(x) = 2x³ - 6x² -9x + 4; k=1

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