Question 1

Which of the following is the greatest common factor (GCF) of the monomials $$18x^2y$ and 24xy^3$?

Accepted Answer

$$6xy$$

Question 2

Factor the polynomial $$14x^2 + 21x$ by factoring out the greatest common factor.

Accepted Answer

$$7x(2x + 3)$$

Question 3

What is the greatest common factor (GCF) of $$30x^3y^2$ and 45x^2$y^4$$?

Accepted Answer

$$15x^2y^2$

Question 4

Factor $$-12x^2 + 8x$ so that the first term inside the parentheses is positive.

Accepted Answer

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

Question 5

Which of the following is the correct factorization of $$25xy - 15x^2$?

Accepted Answer

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

Question 6

Factor the polynomial $$6x^2y$$ + $$9xy^2 by $$factoring out the GCF.

Accepted Answer

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

Question 7

A chemist is mixing two solutions: $$16x^2y$ ml and 24xy^2$ ml. What is the largest volume (in ml) that can be used to equally divide both solutions without leftovers, factoring in both x$ and y$?

Accepted Answer

$$8xy$$

Question 8

Factor $$-18x^2y$$ + $$12xy^2 so $$that the first term inside the parentheses is positive.

Accepted Answer

$$-6xy(3x - 2y)$$

Question 9

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

Accepted Answer

$$(x^2 + 3x) + (2y + 6) = x(x + 3) + 2(y + 3$$)$$

Question 10

Factor $$ax + ay + bx + by by $$grouping.

Accepted Answer

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

Question 11

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

Accepted Answer

$$(x^3$$ + $$2x^2) + (x + 2$$) = $$x^2(x + 2) + 1(x + 2$$) = $$(x^2 + 1)(x + 2$$)$$

Question 12

A medical researcher is analyzing two samples: $$36x^2y^3$ cells and 54x^3$y^2$$ cells. What is the greatest common factor (GCF) of the two sample sizes?

Accepted Answer

$$18x^2y^2$

Question 13

Factor $$12x^2y$$ - $$8xy^2 by $$factoring out the GCF.

Accepted Answer

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

Question 14

Factor $$x^2 - 4x + 2x - 8$ by grouping.

Accepted Answer

$$(x^2 - 4x) + (2x - 8) = x(x - 4) + 2(x - 4) = (x + 2)(x - 4$$)$$

Question 15

Factor $$2xy + 4x - 3y - 6 by $$grouping.

Accepted Answer

$$(2xy + 4x) + (-3y - 6) = 2x(y + 2) - 3(y + 2) = (2x - 3)(y + 2)$$

Question 16

Factor $$3x^2y$$ - $$6xy^2 + 2x - 4y$ by grouping.

Accepted Answer

$$(3x^2y$$ - $$6xy^2) + (2x - 4y) = 3xy(x - 2y) + 2(x - 2y) = (3xy + 2)(x - 2y$$)$$

Question 17

A factory produces $$40x^2y$ widgets and 60xy^2$ widgets. What is the greatest common factor (GCF) of the two production numbers?

Accepted Answer

$$20xy$$

Question 18

Factor $$x^2 - 2x + 3x - 6$ by grouping.

Accepted Answer

$$(x^2 - 2x) + (3x - 6) = x(x - 2) + 3(x - 2) = (x + 3)(x - 2$$)$$

Factoring Polynomials: Greatest Common Factor and Factoring by Grouping

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