Find the value of a, if x – a is a factor of \$x^3 – ax^2 + 2x + a – 1\$.

A) \$2 / 3\$

B) \$1 / 3\$

C) \$4 / 3\$

D) \$5 / 3\$

Divide the polynomial and find the remainder P(x) = \$2x^3 + 3x^2 - 5x + 6\$ by D(x) = x - 2.

A) 10x + 7

B) 9x + 6

C) 9x - 6

D) 10x - 7

Use the factor theorem to determine if x - 3 is a factor of P(x) = \$2x^3 - 9x^2 + 7x - 6\$.

A) x = - 12

B) P(x) = 12

C) x - 3 is a factor

D) There is no factor

Find the zeros of \$f(x) = 4x - 8\$.

A) 6

B) 4

C) 1

D) 2

The length of the rectangle is 2x - 3 and its width is equal to x - 1. Find the area of the rectangle.

A) \$x^2 - 5x + 3\$

B) \$2x^2 - 3x + 3\$

C) \$2x^2 - 5x + 3\$

D) \$3x^2 - 5x + 3\$

Find the quotient when \$3x^4 + 2x^3 - 5x^2 + 4x - 7\$ is divided by x + 2.

A) \$3x^4 - 2x^2 + 11x - 3\$

B) \$x^3 - 7x^2 + 8x - 2\$

C) \$3x^3 - 4x^2 + 3x - 2\$

D) \$5x^3 - 2x^2 + 3x - 9\$

Factor each of the polynomials is \$x^5 - 7x^4 - 2x^3 + 100x^2 - 232x + 160\$.

A) \$ (x-2)^2(x+4)(x-5)\$

B) \$(x - 3) (x^4 - 3x^3 - 12x^2 + 34x - 40)\$

C) \$ (x-1)^2(x+3)(x-4)\$

D) \$(x - 3) (x^4 - x^3 - 11x^2 + 4x - 40)\$

Factor the polynomial \$ x^3 - 3x^2 - 4x + 12\$.

A) \$(x - 3) (x - 2) (x + 2)\$

B) \$(x - 4) (x - 3) (x + 2)\$

C) \$(x - 1) (x - 2) (x + 3)\$

D) \$(x - 1) (x - 3) (x + 5)\$

Determine the values of the local extrema for each of the functions is f(x) = \$4x^5 - 12x^3 + x^2 - 2\$.

A) x = 1

B) x = 0

C) x = 2

D) x = 3

Factor each of the polynomials is \$4x^4 - 16x^3 - 147x^2 + 245x + 1372\$.

A) \$(x - 6) (3x^3 + 14x^2 - 53x - 196)\$

B) \$(x - 7)(x - 4)(2x + 7)^2\$

C) \$(x - 2) (4x^4 + 6x^2 - 73x - 98)\$

D) \$(x - 5) (x^3 + 11x^2 - 43x - 96)\$