9.6 Factoring Trinomials with leading Coeficient
In this section, we will…
Factor out the GCF (Greatest Common Factor)
Factor Trinomials of the Form x 2  bx  c
Factor Trinomials of the Form ax 2  bx  c
Examples: Factor out the GCF (greatest common factor).
60 x2 y  48xy 2  72 x3 y
5(3x  7)  x(3x  7)
factor the polynomial
sum
product
We are,
in essence,
un-FOIL-ing
x2  5x  6
Factoring Trinomials with a leading coefficient of 1:
 Write the trinomial in descending order
(for the first variable alphabetically)
 Write the factorizations of the third term of the trinomial
 Pick the factorization where the sum of the factors is equal to the
coefficient of the middle term.
2
Examples: Factor each trinomial.
x  16  10 x
2
y 2 12 y  36
2
Factoring Polynomials: Factor Trinomials of the Form x + bx
+c
Factoring Trinomials with a leading coefficient other than 1
Guess-and-Check Method
 Write the trinomial in descending order
 Write the factorizations that you know
 Systematically guess-and-check factorization possibilities where the sum of the
factors is equal to the coefficient of the middle term.
(Be sure to check!)
6x  7x  3
2
Factoring Polynomials: Factor Trinomials of the Form ax + bx2 + c
Examples: Factor each trinomial.
8x2  10 x  3
4a 2  9a  9
5x2  4 x  1
18x2  3xy 10 y 2
If a trinomial has the form ax 2  bx  c with integer coefficients and a  0.
2
we can test to see whether it is factorable: If the value of b  4ac is a perfect
square (e.g. 0, 1, 4, 9, 16,…) then the trinomial can be factored using integers.
2bx
Factoring Polynomials: Factor Trinomials
Examples: Factor the polynomial completely.
4a  8a  32
2
Factoring Polynomials
Independent Practice
You learn math by doing math. The best way to learn math is to practice,
practice, practice. The assigned homework examples provide you with an
opportunity to practice. Be sure to complete every assigned problem (or more
if you need additional practice). Check your answers to the odd-numbered
problems in the back of the text to see whether you have correctly solved each
problem; rework all problems that are incorrect.
Homework:
See website
Pretend you’re starring in a reality show about a kid who can
make his dreams come true if he works hard and gets good
grades.
Factoring Polynomials