Download Notes 4-5 Factoring Trinomials

MATD 0390 Intermediate Algebra
Section 4.5: Factoring Trinomials
Christy Dittmar
Factoring Trinomials (4.5)
Finish the diagram by finding two numbers you would multiply to get the top value and add to
get the bottom value. Enter the two numbers on the left and right (in any order)
24
!27
11
6
The AC Method (or the Grouping Method)
Factoring polynomials of the form ax 2 + bx + c or ax 2 + bxy + cy 2
ac
b
•
Find the product ac and fill it in on top.
•
Enter the coefficient b on the bottom.
•
Fill in the left and right as above.
•
Use these numbers (left and right) as coefficients to break apart middle term
•
Factor the resulting four-term polynomial by grouping
Note: If the diagram can be completed, and is completed correctly, factoring by grouping must
work.
If the diagram cannot be completed for a polynomial in this form, the polynomial is prime.
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MATD 0390 Intermediate Algebra
Section 4.5: Factoring Trinomials
Christy Dittmar
Example: 6x 2 + 11x + 3
Factor. 4x 2 + 4x ! 3
6x 2 ! xy !12y 2
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MATD 0390 Intermediate Algebra
Section 4.5: Factoring Trinomials
Christy Dittmar
Be careful about signs Figure out signs of left and right first, then find numbers to fit the signs.
Caution! Example of two polynomials that look similar, but factor differently.
Factor. 6x 2 +13x ! 5
6x 2 !13x + 5
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MATD 0390 Intermediate Algebra
Section 4.5: Factoring Trinomials
Christy Dittmar
Prime polynomials Which of these polynomials is prime?
3x 2 ! 2x ! 8
3x 2 ! 2x + 8
Trial and Errror
Example:
F
x
2
O+I
L
+ 11x + 24
Try to guess the binomials that would FOIL to this result.
•
F must come from x ! x
•
L comes from some factorization of 24
Try different factors until the middle term comes out right.
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MATD 0390 Intermediate Algebra
Section 4.5: Factoring Trinomials
Example:
F
O+I
2x 2 + 5x
Christy Dittmar
L
!3
Try to guess the binomials that would FOIL to this result.
•
F must come from 2x ! x
•
L must come from 3 !1 , one of which is positive and the other negative
Try different factors until the middle term comes out right.
When to use trial and error The trial and error method is likely to be faster if there are not many possibilities to try. Consider
using it in any of these situations:
•
When the first term is x 2 (coefficient of 1)
•
When the first and last coefficients are both prime numbers
•
Anytime, if you find it easy to keep track of the possibilities!
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