4. Polynomial Functions

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) = 2x^3 + 3x^2 - 16x+10; k = -4

In Exercises 17–32, divide using synthetic division. (x^5+x^3−2)/(x−1)

In Exercises 17–32, divide using synthetic division. (x^7+x^5−10x^3+12)/(x+2)

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

Given f(x) = 2x^3 - 7x^2 + 9x - 3, use the Remainder Theorem to find f(- 13).

For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = - x^3 + 8x^2 + 63; k=4

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=x^4+5x^3+5x^2−5x−6;f(3)

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=2x^4−5x^3−x^2+3x+2;f(− 1/2)

In Exercises 33–40, use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x^4+10x^3+5x^2+x+1;f(− 2/3)

Use synthetic division to divide f(x)=x^3−4x^2+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) = 2x^5 - 10x^3 - 19x^2 - 50; k=3

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 -8; k=2

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 + 3x^2 -x + 1; k = 1+i

Find k so that 4x+3 is a factor of 20x^3+23x^2-10x+k.

When 2x^2−7x+9 is divided by a polynomial, the quotient is 2x-3 and the remainder is 3. Find the polynomial.