Determine the values of the local extrema for each of the functions r(x) = \$- 2x^3 + 6x^2 + 4\$.

A) x = 0

B) x = 1

C) x = 3

D) x = 7

Factor the polynomial \$ 2x^3 - 5x^2 − 3x + 6 \$

A) \$ (x-1) \$

B) \$ (x-1)(2x^2-3x-6) \$

C) \$ (2x^2-3x-6) \$

D) None of these

Use synthetic division to divide \$2x^4 - 5x^3 + 3x^2 + 7x − 6\$ by x − 2.find the remainder

A) 1

B) 22

C) 20

D) 12

Given f(x) is a polynomial of degree 4 such that f(1) = 10, f(2) = 20, f(3) = 30, f(4) = 40, find f(5).

A) 8

B) 24

C) 33

D) 70

Given that \$ p(x) = x^3 + ax^2 + bx + c \$ has roots 1,2,and 3, we need to find the value of b − c. when x = 2.

A) 23

B) 45

C) 17

D) 20

If \$(6x + 4y) / (6x - 4y) = 8/6\$ then what is the value of \$x^2 / y^2\$?

A) \$78 / 9\$

B) \$64 / 3\$

C) \$196 / 9\$

D) None

If 4 is a zero of \$f(x) = 3x^3 + kx - 4\$ and 2 is a zero of \$h(x) = 5x^2 - gx + 2\$, what is g - k?

A) 58

B) 24

C) -76

D) -18

Find the degree of the polynomial \$2x^5 + 2x^3y^3 + 4y^4 + 5\$.

A) 6

B) 9

C) 5

D) 3

If one of the zeros of the quadratic polynomial \$(k - 1)x^2 + kx + 1\$ is -3, then the value of k is:

A) \$- 2 / 3\$

B) \$4 / 3\$

C) \$- 4 / 3\$

D) \$2 / 3\$

\$(x^2 + y^2 - z^2)^2 - (x^2 - y^2 + z^2)^2 \$ is equal to:

A) \$4x^2 y^2 z^2\$

B) \$4x^2 y^2 - 4x^2 z^2\$

C) \$x^4 + y^4 + z^4\$

D) 0