4. Polynomial Functions

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

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) = x³ - 2x² - x+2. Use the remainder theorem to find each of the following. Then determine the coordinates 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. (3t²+17t+10)/(3t+2)

Perform each division. See Examples 9 and 10. (4x³-3x²+1)/(x-2)

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

Use synthetic division to perform each division. (5x⁴ +5x³ + 2x² - x-3) / 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)=-3x³+5x-6; k=-1

Use synthetic division to find ƒ(2). ƒ(x)=2x³-3x²+7x-12

Use synthetic division to perform each division. (x⁴ - 3x³ - 4x² + 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) = 3x⁴ + 4x³ - 10x² + 15; k = -1

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x³ - 4x² + 2x+1; k = -1

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 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