Factoring Quadratic Trinomials of the Form
x2+bx+c
Step 1. Set up the problem with two sets of parentheses and factor the x2 term into to factors of x.
(x )(x )
Step 2. List the factor pairs of the c. Make a tree or a table if necessary.
Step 3. Determine which of the factor pairs of c add up to b. Place them in the parentheses using the appropriate positive or negative signs. (You can check your work by doing the FOIL method and comparing it to the original problem.)
Directions: Please factor the following expression.
x2+8x-20
Step 1. Set up the problem with two sets of parentheses and factor the x2 term into to factors of x.
(x )(x )
Step 2. List the factor pairs of the c.
In the problem above c (the last term) is -20. The factors of -20 are
c = -20 |
|||||
| 1 | -20 | ||||
| 2 | -10 | ||||
| 4 | -5 | ||||
| 5 | -4 | ||||
| 10 | -2 | ||||
| 20 | -1 | ||||
Step 3. Determine which of the factor pairs of c add up to b. Place them in the parentheses using the appropriate positive or negative signs.
Sum |
||||||||
| 1 | -20 | -19 | ||||||
| 2 | -10 | -8 | ||||||
| 4 | -5 | -1 | ||||||
| 5 | -4 | 1 | ||||||
| 10 | -2 | 8=b | ||||||
| 20 | -1 | 19 |
(x + 10 )(x - 2)
Directions: Please factor the following expressions. If any of the following expressions cannot be factored, please indicate so by stating "prime".
| 1. x2+5x+4 | 2. x2+12x+32 |
| 3. x2+15x+50 | 4. a2-5a-24 |
| 5. a2+5a-24 | 6. r2+2r-48 |
| 7. x2+6x-72 | 8. d2+2d+80 |
| 9. x2-6x+9 | 10. m2+15m+54 |
| 11. x2-33x+32 | 12. x2-12x+20 |
| 13. b2+b-72 | 14. d2-25d+156 |
| 15. b2-10b+24 | 16. f2-11f-26 |
Directions: Please answer the following.
16. A rectangle has an area of x2-7x+6. What are the dimensions of the rectangle? What are all the possible values for x in this rectangle?
Directions: Please write 1-2 two paragraphs that thoroughly address the following.
1. How can you check to see if you factored correctly? How does this differ from the process by which we check an answer when we solve an equation in one variable?
2. If the third term of a given trinomial is negative, then the factor pairs generated in step 2 must contain one positive factor and one negative factor. How do we determine which factor is negative and which is postive?
What do you do if the coefficient of x2 is not '1'?
Look at Missouri Western State College's Web Page on Factoring Quadratic Trinomials
http://academic.shu.edu/eop/worksheets/exac2127/factoring4a.doc