Question 1

Which of the following is the greatest common factor (GCF) of the polynomial $$9y^4$$ + $$y^2$$?

Accepted Answer

$$y^2$$

Question 2

Factor the polynomial $$6x^2 + 8x - 12x$ completely.

Accepted Answer

$$2x(3x + 4 - 6)$$

Question 3

Which of the following is the correct factorization by grouping for $$mp^2 + 7m$$ + $$3p^2 + 21$?

Accepted Answer

$$(mp^2 + 7m$$) + $$(3p^2 + 21$$)$$

Question 4

Given the trinomial $$4y^2 - 11y + 6$, which of the following is its correct factorization?

Accepted Answer

$$(4y - 3)(y - 2)$$

Question 5

Which of the following is the correct factorization for the difference of squares $$a^2$$ - $$b^2$$?

Accepted Answer

$$(a + b)(a - b)$$

Question 6

Factor the binomial $$x^3 + 27$ completely.

Accepted Answer

$$(x + 3)(x^2$ - 3x + 9)$$

Question 7

Which of the following is the correct factorization for $$m^3$$ - $$64n^3$$?

Accepted Answer

$$(m - 4n)(m^2$ + 4mn + 16n^2$)$$

Question 8

A polynomial is considered prime when:

Accepted Answer

It cannot be factored into polynomials of lower degree with integer coefficients.

Question 9

Which of the following is the correct factorization for $$16p^2 - 40pq$$ + $$25q^2$$?

Accepted Answer

$$(4p - 5q)^2$

Question 10

Factor the expression $$12x^{-2}$$ - $$8x^{-3} by $$factoring out the least power of $$x.$$

Accepted Answer

$$4x^{-3}(3x - 2$$)$$

Question 11

Which of the following is the correct factorization for $$y^3$$ - $$x^3 + 6x - 9$?

Accepted Answer

$$(y - x)(y^2$ + yx + x^2$) + 3(x - 3)$$

Question 12

Which of the following is the correct factorization for $$x^2 + 13x - 18$?

Accepted Answer

Question 13

Which of the following is the correct factorization for $$36x^2y^2$ + 84xy + 49$?

Accepted Answer

$$(6xy + 7)^2$

Question 14

Which of the following is the correct factorization for $$(2a - 1)^2$ + 8$$?

Accepted Answer

$$(2a - 1 + 2	ext{i}\sqrt{2})(2a - 1 - 2	ext{i}\sqrt{2})$$

Question 15

Which of the following is the correct factorization for $$4a^2 - 9$?

Accepted Answer

$$(2a + 3)(2a - 3)$$

Question 16

Which of the following is the correct factorization for $$x^2 - 6x + 9$$ - $$y^4$$?

Accepted Answer

$$(x - 3)^2$ - y^4$

Question 17

Which of the following is the correct factorization for $$6x^4$$ - $$13x^2 - 5$?

Accepted Answer

$$(6x^2$$ + $$1)(x^2 - 5$$)$$

Question 18

Which of the following is the correct factorization for $$8q^4$$ + $$125p^3$$?

Accepted Answer

$$(2q^2$$ + $$5p)(4q^4$$ + $$10q^2p$$ + $$25p^2$$)$$

Question 19

Which of the following is the correct factorization for $$4m^{1/2}$$ + $$3m^{3/2}$$?

Accepted Answer

$$m^{1/2}(4 + 3m$$)$$

Factoring Polynomials in College Algebra: Methods and Applications

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