Name DateWORKSHEET 5.16: FACTORING TRINOMIALS IF THE LAST
TERM IS NEGATIVE
-------------------------------------------------------------------------------------In order to factor trinomials in the formx^2 +bx+c, you must find two integers whose product
iscand whose sum isb.Follow the steps below to factor trinomials if the last term is negative:- List all pairs of the factors ofc.Becausecis negative, one factor in each pair will be
positive and one will be negative. - Choose two factors ofcthat add up tob.
- Place these factors into factored form.
- Check by multiplying the factors.
EXAMPLE
Factorx^2 + 2 x− 3.
The factors of−3:−3 and 1; 3 and−1.
Becauseb= 2 , choose 3 and−1 as the factors ofc.(x+3)(x−1)Check:(x+3)(x−1)=x^2 −x+ 3 x− 3 =x^2 + 2 x− 3
DIRECTIONS: Factor each trinomial. If the trinomial cannot be factored, write ‘‘cannot be
factored.’’- x^2 +x− 6 2. x^2 + 2 x− 8 3. x^2 + 4 x− 5
- x^2 − 5 x− 14 5. x^2 + 5 x− 24 6. x^2 +x− 2
- x^2 − 6 x− 40 8. x^2 +x− 30 9. x^2 − 5 x− 15
- x^2 −x− 12 11. x^2 − 4 x− 32 12. x^2 + 3 x− 10
CHALLENGE:Kelli tried to factorx^2 − 19 x−20 and determined that the
polynomial could not be factored. She found four pairs of factors of−20,
but none added up to−19. Is she correct? Explain your reasoning.207Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.