4. Polynomial Functions

Divide using synthetic division. (x²−5x−5x³+x⁴)÷(5+x)

Divide using long division. $(4x^3-3x^2-2x+1)÷(x+1)$

Divide using synthetic division. (2x⁵−3x⁴+x³−x²+2x−1)/(x+2)

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x² - 3x-3; k = 2

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=3x³−7x²−2x+5;f(−3)

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

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 +7x² + 10x; k=0

Write a polynomial that represents the length of each rectangle. Transcription: The area of the rectangle is 0.5x³ - 0.3x² + 0.22x + 0.06 square units and its width is x + 0.2 units

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 - 2x + 2; k = 1-i

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) = 4x⁴ + x² + 17x + 3; k= -3/2

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 (1)

Use synthetic division to show that 5 is a solution of x^4−4x^3−9x^2+16x+20=0. Then solve the polynomial equation.

Perform each division. See Examples 7 and 8. $(-4m^2{n}^2-21m{n}^3+18m{n}^2)/(-14m^2{n}^3)$

Perform each division. See Examples 9 and 10. (p²+2p+20)/(p+6)

Perform each division. See Examples 9 and 10.

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