Review these concepts at Factoring Expressions Study Guide.
Factoring Expressions Practice Questions
Problems
Practice 1
Factor each expression.
 6x + 2
 5x^{2} + x
 15y – 20y^{4}
 –2x^{5} + 4x^{4}
 13h^{2} – 13h
 a^{4} – a^{3} + a^{2}
 6s + 15s^{4}– 21s^{8}
 14z^{6}– 35z^{9}–42z^{4}
 9p^{3} + 27p^{5} – 6p^{10}+ 12p^{12}
 –20q^{8}–8q^{20} –40q^{12}– 80q^{10}
Practice 2
Factor each expression.
 18g^{8}h^{2}– 45g^{2}h^{8}
 –36x^{7}y^{3} + 12y^{2}
 5a^{9}bc^{3} – 11a^{6}b^{5}c^{5}
 6j^{11}k^{3}l^{2} + 48j^{7}k^{10}l^{4}– 28j^{9}k^{6}l^{6}
 50r^{5}t^{4} + 35s^{5}t^{4} + 45r^{5}s^{5}t^{4}
Solutions
Practice 1
 The factors of 6x are x, 1, 2, 3, and 6, and the factors of 2 are 1 and 2. Both numbers have 2 as a common factor, so we can factor a 2 out of each term.
Only the first term has an x, so we cannot factor out an x.
Divide both terms by 2: 6x ÷ 2 = 3x, and 2 ÷ 2 = 1.
Write 2 outside the parentheses to show that both terms are multiplied by it: 2(3x + 1).
 The factors of 5x^{2} are x^{2}, 1, and 5, and the factors of x are 1 and x. Both terms have x as a common factor, so we can factor an x out of each term.
Divide both terms by 5x^{2} ÷ x = 5x, and x ÷ x = 1.
Write x outside the parentheses to show that both terms are multiplied by it: x(5x + 1).
 The factors of 15y are y, 1, 3, 5, and 15, and the factors of 20y4 are y4, 1, 2, 4, 5, 10, and 20. Both terms have 5 and y as common factors, so we can factor 5y out of each term.
Divide both terms by 5y: 15y ÷ 5y = 3, and 20y^{4} ÷ 5y = 4y^{3}.
Write 5y outside the parentheses to show that both terms are multiplied by it: 5y(3 – 4y^{3}).
 The factors of –2x^{5} are –1, 2, x^{5}, and the factors of 4x^{4} are 1, 2, 4, and x^{4}.
Both terms have 2 and x as common factors. In fact, we can factor 2x^{4} out of both terms.
Divide both terms by 2x^{4}: –2x^{5} ÷ 2x^{4} = –x, and 4x^{4} ÷ 2x^{4} = 2.
–2x^{5} + 4x^{4} factors into 2x^{4}(–x + 2).
 The factors of 13h^{2} are h^{2}, 1, and 13, and the factors of 13h are h, 1, and 13.
Both terms have 13 and h as common factors.
Divide both terms by 13h: 13h^{2} ÷ 13h = h, and 13h ÷ 13h = 1.
13h^{2} – 13h factors into 13h(h – 1).
 Each term in a^{4} – a^{3} + a^{2} has no coefficient, but a is a common factor of every term. The smallest exponent of a is 2, in the term a^{2}.
Divide every term by a^{2}: a^{4} ÷ a^{2} = a^{2}, a^{3} ÷ a^{2} = a, and a^{2} ÷ a^{2} = 1.
a^{4} – a^{3} + a^{2} factors into a^{2}(a^{2} – a + 1).
 The greatest common factor of 6, 15, and 21 is 3. Every term has s as a common factor, and the smallest exponent of s is 1, in the term 6s.
Divide every term by 3s: 6s ÷ 3s = 2, 15s^{4} ÷ 3s = 5s^{3}, and 21s^{8} ÷ 3s = 7s^{7}.
6s + 15s^{4} – 21s^{8} factors into 3s(2 + 5s^{3} – 7s^{7}).
 The greatest common factor of 14, 35, and 42 is 7. Every term has z as a common factor, and the smallest exponent of z is 4, in the term 42z^{4}.
Divide every term by 7z^{4}:14z^{6} ÷ 7z^{4} = 2z^{2}, 35z^{9} ÷ 7z^{4} = 5z^{5}, and 42z^{4} ÷ 7z^{4} = 6.
14z^{6} – 35z^{9} – 42z^{4} factors into 7z^{4}(2z^{2} – 5z^{5} – 6).
 The greatest common factor of 9, 27, 6, and 12 is 3. Every term has p as a common factor, and the smallest exponent of p is 3, in the term 9p^{3}.
Divide every term by 3p^{3}: 3p^{3} ÷ 3p^{3} = 3, 27p^{5} ÷ 3p^{3} = 9p^{3}, 6p^{10} ÷ 3p^{3} = 2p7,and 12p^{12} ÷ 3p^{3} = 4p^{9}.
9p^{3} + 27p^{5} – 6p^{10} + 12p^{12} factors into 3p^{3}(3 + 9p^{2} – 2p^{7} + 4p^{9}).
 The greatest common factor of 20, 8, 40, and 80 is 4. Since every term is negative, –1 should be factored out of the expression, too. Every term has p as a common factor, and the smallest exponent of q is 8, in the term –20q^{8}.
Divide every term by –4q^{8}: –20q^{8} ÷ –4q^{8} = 5, –8q^{20} ÷ –4q^{8} = 2q^{12}, –40q^{12} ÷ –4q^{8} = 10q^{4}, and –80q^{10} ÷ –4q^{8} = 20q^{10}.
–20q^{8} – 8q^{20} – 40q12 – 80q^{10} factors into –4q^{8}(5 + 2q^{12} + 10q^{4} + 20q^{2}).

1
 2
Ask a Question
Have questions about this article or topic? AskRelated Questions
See More QuestionsPopular Articles
 Kindergarten Sight Words List
 First Grade Sight Words List
 Child Development Theories
 10 Fun Activities for Children with Autism
 Social Cognitive Theory
 Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
 Signs Your Child Might Have Asperger's Syndrome
 Theories of Learning
 Definitions of Social Studies
 A Teacher's Guide to Differentiating Instruction