Question 1

What is the greatest common factor (GCF) of the terms $$18x^3y^2$ and 24x^2$y^4$$?

Accepted Answer

$$6x^2y^2$

Question 2

Factor the polynomial $$15x^2y$$ - $$10xy^2 by $$factoring out the greatest common factor.

Accepted Answer

$$5xy(3x - 2y)$$

Question 3

Which of the following is the correct first step to factor $$8x^3$$ + $$12x^2 - 4x$?

Accepted Answer

Factor out $$4x$$

Question 4

Given the polynomial $$x^3$$ + $$2x^2 + 3x + 6$, factor it by grouping.

Accepted Answer

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

Question 5

A chemical reaction produces a polynomial $$12a^2b$$ - $$8ab^2 + 4ab$. Factor out the greatest common factor.

Accepted Answer

$$4ab(3a - 2b + 1)$$

Question 6

Which of the following polynomials can be factored by grouping?

Accepted Answer

$$x^3$$ + $$2x^2 + 3x + 6$

Question 7

Factor the polynomial $$6x^2y$$ - $$9xy^2 + 3xy$ completely.

Accepted Answer

$$3xy(2x - 3y + 1)$$

Question 8

A medical researcher models a dosage with the polynomial $$20t^3$$ - $$15t^2 + 10t$. What is the factored form?

Accepted Answer

$$5t(4t^2 - 3t + 2$$)$$

Question 9

Factor the following by grouping: $$ax + ay + bx + by.$$

Accepted Answer

$$(a + b)(x + y)$$

Question 10

Which is the correct factored form of $$-6x^2 + 9x$?

Accepted Answer

$$-3x(2x - 3)$$

Question 11

A factory's profit is modeled by $$14x^2y$$ + $$21xy^2 - 7xy$. Factor completely.

Accepted Answer

$$7xy(2x + 3y - 1)$$

Question 12

Which of the following is NOT a correct step in the factoring by grouping procedure?

Accepted Answer

Combine all terms into a single group before factoring

Question 13

Factor the polynomial $$x^2y$$ + $$2xy^2$$ + $$3y^2 + 6y$ by grouping.

Accepted Answer

$$y(x^2 + 2xy$$) + $$3(y^2 + 2y) = yx(x + 2) + 3y(y + 2) = (x + 2)(xy + 3y$$)$$

Question 14

If a polynomial has no common factor other than 1, what is the next recommended factoring method?

Accepted Answer

Try factoring by grouping

Question 15

Factor $$x^3$$ - $$x^2 + 4x - 4$ by grouping.

Accepted Answer

$$(x^2(x - 1) + 4(x - 1$$)) = $$(x^2 + 4)(x - 1$$)$$

Question 16

A business's revenue is modeled by $$30x^2y$$ - $$45xy^2 + 15xy$. Factor completely.

Accepted Answer

$$15xy(2x - 3y + 1)$$

Question 17

Which of the following is the GCF of $$28x^4y^2$ and 35x^2$y^3$$?

Accepted Answer

$$7x^2y^2$

Question 18

Factor $$x^2 - 4x + 3$ by first factoring out the GCF, if possible.

Accepted Answer

No GCF other than 1; factor as $$(x - 1)(x - 3)$$

Factoring in Intermediate Algebra: Greatest Common Factors and Factoring by Grouping

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