Aim: How Do We Factor Trinomials?
Do Now:
• Multiply
1) (x+8)(x+4)
2) (x-8)(x-3)
3) (x-8)(x+1)
4) (x+9)(x-5)
Factoring Simple Trinomials
A simple trinomial is of the form ax2 + bx + c.
The middle term of a simple trinomial is the sum of
the last two terms of the binomials.
The last term is the product of the last two terms of
the binomials.
The method used is the sum/product method.
Look for two numbers that have a product equal to
the last term and a sum equal to the numerical
coefficient of the middle term.
Factoring Simple Trinomials
Factor:
6a2 + 42a + 72
= 6(a2 + 7a + 12)
= 6(a + 4)(a + 3)
a2 + 9ab + 20b2
= (a + 4b)(a + 5b)
Factoring
ax  bx  c, a  1
2
Factoring General Trinomials
Factor: 3x2 + 17x + 10
3 2
x  17 x  10(3)
3
x  17 x  30
2
Divide 1st term by the leading
coefficient and multiply the last
term by the leading coefficient
Simplify
( x + 15)( x + 2)
Factor x2 + 17x + 30 and leave
a space before each x
(3x + 15)(3x + 2)
Put 3 back into each binomial
(x + 5)(3x + 2)
Divide each binomial by the
GCF if there is (are)
Factor: 3x2 - 10x - 8
3 2
x  10 x  8(3)
3
x  10 x  24
2
Divide 1st term by the leading
coefficient and multiply the
last term by the leading
coefficient
Simplify
( x – 12)( x + 2)
Factor x2 + 17x + 30 and
leave a space before each x
(3x – 12)(3x + 2)
Put 3 back into each binomial
(x – 4)(3x + 2)
Divide each binomial by the
GCF if there is (are)
Factor the following trinomials
1. 6x2 + x – 15
( x + 10)( x – 9)
x2 + x – 90
(6x + 10)(6x – 9)
(3x + 5)(2x – 3)
2. 12x2 – 9x – 3
3(4x2 – 3x – 1) 3(x2 – 3x – 4) 3( x +1)( x – 4)
3(4x + 1)(4x – 4)
3(4x + 1)(x – 1)
3. 3x2 + 20x + 12
x2 + 20x + 36
(x + 6)(3x + 2)
(3x + 18)(3x + 2)
Factor: 5(4 – 3x) + 8x(4 – 3x)
=(4 – 3x)(5 + 8x)
Factor: 2(5x + 2)2 – 7(5x + 2)
=(5x + 2)[2(5x + 2) – 7]
=(5x + 2)(10x + 4 – 7)
=(5x + 2)(10x – 3)
Factoring Expressions With Complex Bases
(a + 2)2 + 3(a + 2) + 2
Let A = (a + 2).
A2 + 3A + 2
= (A + 2)(A + 1)
Replace (a + 2) with A.
Factor the trinomial.
= [(a + 2) + 2] [(a + 2) + 1]
Replace (a + 2) with A.
= (a + 4)(a + 3)
Simplify.
5x  x  5x  1
3
2
(5 x  x )  (5 x  1)
3
2
Group into two
binomials
x (5 x  1)  (5 x  1)
Factor by GFC if
possible
(5 x  1)( x  1)
Factor by GFC
(5 x  1)( x  1)( x  1)
Factor completely
2
2
Factor each trinomial if possible.
1) x2 –10x + 24
2) x2 + 3x – 18
3) 2x2 – x – 21
4) 3x2 + 11x + 10
5) 5(2x – 3)2 + 9(2x – 3)
6) (x – 3)2 – 6(x – 3) + 8
7) x3 + 3x2 – x – 3