4. Polynomial Functions

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

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

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

Perform each division. See Examples 9 and 10. (q²+4q-32)/(q-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)=-3x³+5x-6; k=-1

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x²−2x+5)/(x−3)

Use synthetic division to perform each division. (-9x³ + 8x² - 7x+2) / x-2

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

Divide using synthetic division. (4x³−3x²+3x−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) = 3x⁴ + 4x³ - 10x² + 15; k = -1

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) = x² + 4; k = 2i

Perform each division. See Examples 9 and 10.

$\frac{(10x^3+11x^2-2x+3)}{(5x+3)}$

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 + 3x + 4; k = 2+i