4. Polynomial Functions

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 + 3x + 4; k = 2+i

The remainder theorem indicates that when a polynomial ƒ(x) is divided by x-k, the remainder is equal to ƒ(k). Consider the polynomial function ƒ(x) = x^3 - 2x^2 - x+2. Use the remainder theorem to find each of the following. Then determine the coor-dinates of the corresponding point on the graph of ƒ(x). ƒ (-2)

Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-14x^2)/(-2x^2)

Perform each division. See Examples 9 and 10. (3t^2+17t+10)/(3t+2)

Perform each division. See Examples 9 and 10. (4x^3-3x^2+1)/(x-2)

Use synthetic division to perform each division. (5x^4 +5x^3 + 2x^2 - x-3) / x+1

Use synthetic division to perform each division. (x^4 - 3x^3 - 4x^2 + 12x) / x-2

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) = 3x^4 + 4x^3 - 10x^2 + 15; k = -1

For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = x^3 - 4x^2 + 2x+1; k = -1

For each polynomial function, use the remainder theorem to find ƒ(k).ƒ(x) = 6x^4 + x^3 - 8x^2 + 5x+6; k=1/2

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 + 4x -4; k=2