Name DateWORKSHEET 5.15: FACTORING TRINOMIALS IF THE LAST
TERM IS POSITIVE
-------------------------------------------------------------------------------------When factoring trinomials in the formx^2 +bx+c, you must find two factors ofcwhose sum
equalsb. Follow the steps below to factor trinomials if the last term is positive:- List all the pairs of factors ofc.
- Considerb, the coefficient ofx.
- Ifbis positive, choose the two positive factors ofcwhose sum equalsb.
- Ifbis negative, choose the two negative factors ofcwhose sum equalsb.
- Place these factors into factored form.
- Check by multiplying the factors.
EXAMPLE
Factorx^2 + 7 x+ 10.
The factors of 10: 1 and 10; 2 and 5;−1and−10;−2and−5.
Becauseb=7, choose 2 and 5 as the factors ofc.(x+2)(x+5)Check:(x+2)(x+5)=x^2 + 5 x+ 2 x+ 10 =x^2 + 7 x+ 10
DIRECTIONS: Factor each trinomial. If the trinomial cannot be factored, write ‘‘cannot be
factored.’’- x^2 + 6 x+ 5 2. x^2 + 6 x+ 8 3. x^2 − 5 x+ 6
- x^2 − 9 x+ 20 5. x^2 + 7 x+ 10 6. x^2 + 23 x+ 22
- x^2 − 10 x+ 30 8. x^2 − 7 x+ 12 9. x^2 + 8 x+ 15
- x^2 − 17 x+ 16 11. x^2 + 8 x+ 12 12. x^2 − 13 x+ 40
CHALLENGE:Kim told James that ifcis positive and he told her the sign ofb,
she would tell him the signs of their factors. How could she know this
without knowing the actual value ofb?205Copyright
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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.