Download 3 Factoring Trinomials

8-3A Factoring Quadratic
Trinomials
There are numerous methods to factor trinomials.
The method used in this presentation is NOT in your
textbook. Please pay attention as this method is
easier to use than the method presented in the book!
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
In the previous lesson, you solved a quadratic equation
by factoring.
The problem.
Set each factor equal
to zero and solve!
x  3x  5  0
x 3  0
x  3
or
x5  0
or
x  5
The factors were given information. Today you will
need to find the factors of a quadratic trinomial.
x+2
Factoring quadratic trinomials means finding the binomial
factors when given a product. The factors represent the
length and width of the rectangle.
x2  5x  6
x 3
x  3x  2
You need to
find the
factors!
You are given the
product –
quadratic trinomial!
x+3
Because multiplication is commutative, it will not matter
what order you write the factors.
x2  5x  6
x 2
x  2x  3
You
to
The need
factors
findchanged
the
have
factors!
order!
This is the
same
quadratic
trinomial
Algebra tiles are not very practical for finding factors of
a quadratic trinomial. Using what you know about product
and sum puzzles will help you to factor trinomials when
the leading coefficient is 1.
x2  6x  7
ax2  bx  c
leading
coefficient
standard form
for a quadratic
trinomial
Factor.
Multiply a times c to find the product.
ax2  bx  c
15
x2  8x
8  15  5  3
Draw an X
on your
x
x

b in the bottom represents
the sum
paper.
To fill in the sides of the x you must find two
This
quadratic
numbers that have
a product
of trinomial
15 and a sum of 8.
is an
expression.
Place the values from
the
sides of theHow
X figure into
do you know it is NOT
your factors.
an equation?
Check by doing
You know
FOIL in your
there will be
head!
an x in each
factor!
All of today’s problems involving quadratic trinomials will
have a leading coefficient of 1.
Multiply a times c to find the product.
–3
ax2  bx  c
x2 
–22x  3 –33  1
x x 
b in the bottom represents the sum
To fill in the sides of the x you must find two
numbers that have a product of –3 and a sum of –2.
Place the values from the sides of the X figure into
your factors.
Check by doing
You know
FOIL in your
there will
head!
be an x in
each factor!
Example 1 Factor.
1. Write the problem.
2. Draw an X next to
the problem.
ax2  bx  c
x2  7x  12
x x 
12
+4
4 +3
3
7
3. Multiply a times c to find the product.
4. Write b in the bottom to represent the sum.
5. Fill in the sides of the x by finding two
numbers that have a product of the top
Check by
number and a sum of the bottom number.
doing FOIL
6. Using the values from the sides of
in your
the X figure write the factors. Your
head!
factors must be in parentheses!
Factor.
Example 2
Example 3
x  9x  20
x2  8x  9
Example 4
Example 5
2
x2  3x  18
x2  6x  7
Factor.
Example 3
Example 2
x2  9x  20
x  5x  4 
20
–5
–4
–9
x2  8x  9
–9
x  9x  1 –9 1
–8
Check by
doing
FOIL in
your head!
Your binomial factors must be in parentheses!
Factor.
Example 4
Example 5
–18
x2  3x  18
x  6x  3 6 –3
3
x2  6x  7
x  7 x  1
Check by
doing FOIL
in your
head!
–7
7 –1
6
Factor.
1) x2  4x  3
x  1x  3
2) x2  5x  4
x  1x  4 
6) x2  4x  4
x  2x  2
7 ) x2  3x  10
x  5x  2
3) x2  5x  6
x  6x  1
8) x2  2x  8
x  4 x  2
4) x2  x  6
x  3x  2
9) x2  8x  7
x  1x  7 
5) x2  5x  6
x  2x  3
10) x2  8x  7
x  7 x  1
8-A5 Handout A5 and Page 439 # 49, 51- 53, 58-63.