4. Polynomial Functions

Divide using long division. State the quotient, and the remainder, r(x). (x³+5x²+7x+2)÷(x+2)

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(6x^3+7x^2+12x-5)÷(3x-1)$

Use synthetic division to perform each division. (x³ + 3x² +11x + 9) / x+1

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x²−2x+5)/(x−3)

Divide using long division. State the quotient, and the remainder, r(x). (4x⁴−4x²+6x)/(x−4)

Use synthetic division to perform each division. (3x³+6x²-8x+3)/(x+3)

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)=5x³-3x²+2x-6; k=2

Divide using long division. State the quotient, and the remainder, r(x). (x⁴+2x³−4x²−5x−6)/(x²+x−2)

Use synthetic division to perform each division. (-9x³ + 8x² - 7x+2) / x-2

Divide using long division. State the quotient, and the remainder, r(x).$\frac{2x^5 - 8x^4 + 2x^3 + x^2}{2x^3 + 1}$

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

Divide using synthetic division. (4x³−3x²+3x−1)÷(x−1)

Divide using synthetic division. (6x⁵−2x³+4x²−3x+1)÷(x−2)

Use synthetic division to perform each division. x⁷+1 / 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) = 2x³ + 3x² - 16x+10; k = -4