Transcript factors

factoring trinomials: ax2 + bx + c
pp 138-139, text
OBJECTIVE:
 find the factors of a trinomial of the
form ax2 + bx + c
factoring trinomials: ax2 + bx + c
Review of past lessons
 factors: numbers or variables that
make up a given product
 GCF: greatest number that could be
found in every set of factors of a
given group numbers
 binomial: a polynomial of two terms
 trinomial: a polynomial of three terms
factoring trinomials: ax2 + bx + c
Review of past lessons
 coefficient:the numerical factor next to a
variable
 exponent: the small number on the upper
hand of a factor that tells how
many times it will used as
factor
 binomial: a polynomial of two terms
 trinomial: a polynomial of three terms
factoring trinomials: ax2 + bx + c
Review of past lessons
( x + 4)2 = x2 + 4x + 16
( b - 3)2 = b2 - 6b + 9
( y - 5) ( y + 3) = y2 - 2y -15
( m - 7)( m + 7) = m2 - 49
(
a2+16a+64) =
2
=
(a
+
8)
(a + 8)( a + 8 )
( 4a2+20a+24) = 4( a2 +5a + 6 )
factoring trinomials: ax2 + bx + c
(4a2+20a+24) = 4 ( a2 +5a + 6 )
= 4 (a2 + 5a + 6)
= 4 ( a + 3) ( a + 2 )
Example 1. Factor 12y2 – y – 6
12y2 – y – 6
Find the product of the coefficient of
the first term (12) and the last term (–6).
12(-6) = -72
Find the factors of -72 that will add up
to -1.
-72 = -9, 8
-9 + 8 = -1
Use the factors -9 and 8 for the
coefficient of the middle term (-1)
12y2 + (– 9 + 8)y – 6
Use the DPMoA
12y2 + (– 9y + 8y) – 6
Remove the parenthesis.
12y2 – 9y + 8y – 6
Group terms that have common
monomial factors
(12y2 – 9y) + (8y – 6)
3y(4y – 3)
Factor each binomial using
GCF.
+ 2 (4y – 3)
(4y – 3y) ( 3y + 2)
Use the Distributive
Property.
The factored form of 12y2 – y – 6
Example 2. Factor 3x2 + 4x + 1
3x2 + 4x + 1
3(1) = 3
Find the product of the coefficient of
the first term (3) and the last term (1).
Find the factors of 3 that will add up to 4.
3 = 3,1
3+1=4
3x2 + (3+ 1)x + 1
3x2 + (3x+ x) + 1
Use the factors 3 and 1 for the
coefficient of the middle term (4)
Use the DPMoA
Remove the parenthesis.
3x2 + 3x + x + 1
(3x2 + 3x) + (x + 1)
3x (x + 1) + (x+1)
(x + 1) ( 3x + 1)
Group terms that have common
monomial factors
Factor each binomial using GCF.
Use the Distributive Property.
The factored form of 3x2 + 4x + 1.
Example 3. Factor completely 21y2 – 35y – 56.
21y2 – 35y – 56
7(3y2 – 5y – 8)
-24
Factor out the GCF.
Factor the new polynomial, if
possible. Find the product of 3 and -8.
Find the factors of -24 that will add up to
-5 which is the middle term.
-24 = - 8, 3
Use the -8 + 3 in place of -5 in the
middle term.
7[3y2 + (– 8 + 3)y – 8]
Remove the parenthesis.
7[3y2 – 8y + 3y – 8]
Group terms that have common
monomial factors
7[3y2 – 8y + 3y – 8]
Group terms that have common
monomial factors
7[(3y2 – 8y) + (3y – 8)]
Take out the GCF from the
first binomial.
7[y(3y – 8) + (3y – 8)]
Use the Distributive Property.
7 (3y – 8) ( y + 1)
The factored form of 12y2 – y – 6.
factoring trinomials: ax2 + bx + c
pp 138-139, text
Classwork
p 163, Practice book
homework
p 164, Practice book