1.) State the quotient and remainder when the first polynomial is divided by the second. Check your division by calculating (Divisor)(Quotient) + Remainder.

x⁵ - x³ + x - 8 x - 4

What is Quotient ________________ & Remainder____________.

2.) Find the remainder when f(x) is divided by g(x), without using long division.

f(x) = x⁸ - 4 g(x) = x + 3

What is the correct answer? Show your work?

3.)Find the remainder when f(x) is divided by g(x), without using division.

f(x) = 4x⁹⁰ - 4x⁷⁰ + 5x⁵⁰ + 5x³⁴ - 3x¹⁸ + 9 g(x) = x - 1

What is the correct answer? Show your work?

4.) Find a number k satisfying the given condition.

x + 1 is a factor of x³ - kx² + 4x + 4k

k=___________________? Show your work.

5.) State the quotient and remainder when the first polynomial is divided by the second. Check your division by calculating (Divisor)(Quotient) + Remainder. (Enter the remainder as a rational expression.)

x⁴ - 1 x - 1

What is Quotient ________________ & Remainder____________.

6.) Find a polynomial with the given degreen, lead coefficient 1, the given roots, and no other roots.

n= 3 roots2,-3

f(x)=___________________? show your work.

7.) Find a number k satisfying the given condition.

x - 2 is a factor of x⁴ - 2x³ - kx² + 2x - 4

k=_______________? show your work.