Question

Which polynomial is prime?

3x3 + 3x2 – 2x – 2
3x3 – 2x2 + 3x – 4
4x3 + 2x2 + 6x + 3
4x3 + 4x2 – 3x – 3



Factor 15x3 – 5x2 + 6x – 2 by grouping. What is the resulting expression?

(5x2 + 2)(3x – 1)
(5x2 – 2)(3x + 1)
(15x2 + 2)(x – 1)
(15x2 – 2)(x + 1)



Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?

x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)



Factor x3 – 4x2 + 7x – 28 by grouping. What is the resulting expression?

(x2 – 4)(x + 7)
(x2 + 4)(x – 7)
(x2 – 7)(x + 4)
(x2 + 7)(x – 4)



Which shows one way to determine the factors of x3 + 11x2 – 3x – 33 by grouping?

x2(x + 11) + 3(x – 11)
x2(x – 11) – 3(x – 11)
x2(x + 11) + 3(x + 11)
x2(x + 11) – 3(x + 11)

Answer 1

1) Which polynomial is prime?
Answer: None — all four are factorable.
- 3x^3 + 3x^2 – 2x – 2 = (3x^2 – 2)(x + 1)
- 3x^3 – 2x^2 + 3x – 4 = (x – 1)(3x^2 + x + 4)
- 4x^3 + 2x^2 + 6x + 3 = (2x^2 + 3)(2x + 1)
- 4x^3 + 4x^2 – 3x – 3 = (4x^2 – 3)(x + 1)

2) Factor 15x^3 – 5x^2 + 6x – 2 by grouping.
Answer: (5x^2 + 2)(3x – 1)

3) Which shows one way to determine the factors of x^3 – 9x^2 + 5x – 45 by grouping?
Answer: x(x^2 + 5) – 9(x^2 + 5)

4) Factor x^3 – 4x^2 + 7x – 28 by grouping.
Answer: (x^2 + 7)(x – 4)

5) Which shows one way to determine the factors of x^3 + 11x^2 – 3x – 33 by grouping?
Answer: x^2(x + 11) – 3(x + 11)