Question

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 a quotient + 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 evaluate P(c).

P(x) = x⁴ + 7x³ − 6x − 12,     c = −1

f(−1) =

7.

Use the Remainder Theorem to evaluate P(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 with complex coefficients.

9.

Consider the following.

P(x) = x³ + 2x² − 3x − 10

Factor the polynomial as a product of linear factors with complex coefficients.

10.

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

12.

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

f(x) = 6x³ + x² − 41x + 30;    x + 3

x =

13.

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

f(x) = 3x³ − 17x² + 30x − 16;    x − 1

x =

14.

Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-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 your answers as a comma-separated list. Enter all answers including repetitions.)

x =

?

(b) Factor P completely.

P(x) =

?

Answer 1