3. Find the quotient and remainder using long division. x3 + 7x2? x + 1 x + 8

quotient = ?

remainder = ?

4. Simplify using long division. (Express your answer as aquotient + remainder/divisor.)

f(x) =8x² ? 6x + 3

g(x) = 2x+ 1

5.

Find the quotient and remainder using long division.

9x3 + 3x2 + 22x

3x2 + 5

quotient
remainder

6.

Use the Remainder Theorem to evaluateP(c).

P(x) = x⁴ + 7x³ ? 6x ?12,     c = ?1

f(?1) =

7.

Use the Remainder Theorem to evaluateP(c).

P(x) = 9x⁵ ? 3x⁴ + 4x³ ?2x² + x ? 6,    c = ?6

P(?6) =

8.

Consider the following.

P(x) = x³ ? 9x² + 27x ? 27

Factor the polynomial as a product of linear factors withcomplex coefficients.

9.

Consider the following.

P(x) = x³ + 2x² ? 3x ? 10

Factor the polynomial as a product of linear factors withcomplex coefficients.

10.

Thepolynomial  P(x) =5x²(x ?1)³(x + 9) has degree (?). It haszeros 0, 1, and (?). The zero 0 has multiplicity (?), and the zero1 has multiplicity (?). (answer all (?)

12.

Use the Factor Theorem to find all real zeros for the givenpolynomial function and one factor. (Enter your answers as acomma-separated list.)

f(x) = 6x³ + x² ? 41x +30;    x + 3

x =

13.

Use the Factor Theorem to find all real zeros for the givenpolynomial function and one factor. (Enter your answers as acomma-separated list.)

f(x) = 3x³ ? 17x² + 30x ?16;    x ? 1

x =

14.

Use the Factor Theorem to find all real zeros for the givenpolynomial function and one factor. (Enter your answers as acomma-separated list.)

2x³ + 7x² ? 12x ?42;    2x + 7

x =

15.

A polynomial P is given.

P(x) = x³ + x² + 3x

(a) Find all zeros of P, real and complex. (Enter youranswers as a comma-separated list. Enter all answers includingrepetitions.)

x =

?

(b) Factor P completely.

P(x) =

?