The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 5.18: FACTORING TRINOMIALS IF THE LEADING

COEFFICIENT IS AN INTEGER GREATER THAN 1

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Follow the steps below to factor trinomials written asax^2 +bx+cwhen the leading

coefficient is an integer greater than 1:

1. Find the product ofaandc.List the factors of the product.


2. Find a pair of factors whose sum isb.(If the sum cannot be found, the trinomial cannot
   be factored.)


3. Expressbxas the sum found in step 2 and substitute these values in the trinomial.


4. Factor by grouping.


5. Check by multiplying the factors.

EXAMPLE

Factor 5 x^2 − 18 x− 8.

ac=−40. The pairs of factors of−40 are 1,−40;−1, 40; 2,−20;−2, 20; 4,−10;−4, 10; 5,−8;

−5, 8.

Becauseb=− 18 , select 2 and−20 because 2+(−20)=−18.

bx= 2 x− 20 x. Substitute 2x− 20 xforbxto get 5 x^2 + 2 x− 20 x− 8.

Factor by grouping(5x^2 + 2 x)−(20x+8)=x(5x+2)−4(5x+2)=(5x+2)(x−4).

Check:(5x+2)(x−4)= 5 x^2 − 20 x+ 2 x− 8 = 5 x^2 − 18 x− 8

DIRECTIONS: Factor the trinomial. If the trinomial cannot be factored, write ‘‘cannot be

factored.’’

1. 2 x^2 + 7 x+ 6 2. 3 x^2 + 14 x− 5 3. 3 x^2 + 7 x+ 1


2. 8 x^2 + 2 x− 3 5. 6 x^2 + 7 x− 3

CHALLENGE:When factoring 6x^2 −x−1, Ronnie said that he found all the

factors of 6. He said that the polynomial could not be factored because

there is no pair of factors of 6 that has a sum equal to−1. Is he correct?

Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.