4. Polynomial Functions

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

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

Use synthetic division to perform each division. $\frac{\frac{1}{3}{x}^3-\frac{2}{9}{x}^2+\frac{2}{27}x-\frac{1}{81}}{x-\frac{1}{3}}$

Use synthetic division to perform each division. (x⁴ - 3x³ - 4x² + 12x) / x-2

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.

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 -8; k=2

Use synthetic division and the Remainder Theorem to find the indicated function value. f(x)=6x⁴+10x³+5x²+x+1; f(−2/3)

Perform each division. See Examples 7 and 8. $(8wx{y}^2+3w{x}^{2}y+12w^{2}xy)/\left(4w{x}^{2}y\right)$

Perform each division. See Examples 9 and 10.

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

Divide using synthetic division. (6x⁵−2x³+4x²−3x+1)÷(x−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) = 4x⁴ + x² + 17x + 3; k= -3/2

Divide using long division. State the quotient, and the remainder, r(x). (x⁴−81)/(x−3)

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

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