Download 3-Solving Quadratics

8-3B Factoring Trinomials and
Solving Quadratic Equations
The standard form of a quadratic equations is
2
ax  bx  c  0
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
In a previous lesson you solved quadratic equations by
setting factors equal to zero and solving. The factors were
given to you. Now you know how to find the factors.
Solve the equation.
Write in standard form.
Factor
Set each factor equal
to zero and solve!
x2  7  6x
x2  6x  7  0
x  7 x  1  0
x  7  0 or x  1  0
x  7
x 1
Check both
solutions in the
original equation!
–7
7 –1
6
Students sometimes confuse the instructions. Make
sure you understand what it means to:
Factor a quadratic
expression.
2
x  8x  15
x  5x  3
15
5 3
8
Solve a quadratic
equation.
x2  8x  15  0
x  5x  3  0
15
5 3
8
x 5  0 x 3  0
x  3
x  5
factors
solution
s
Find two consecutive integers x and x + 1 with
a product of 72.
x  x  1  72
-72
x2  x  72
9 -8
x2  x  72  0
1
x  9x  8  0
x  9  0 or x  8  0
x8
x  9
The numbers are -9 and -8,
or the numbers are 8 and 9.
Write in standard form before factoring.
A triangle has an area of 130 square cm. Find the
height, h, of the triangle if the base is (2h + 6) cm.
1
A  bh
2
1
h
130  2h  6h
2
130  h  3h
2h + 6
-130
130  h2  3h
13 -10
0  h2  3h  130
3
0  h  13h  10 
h  13  0 or h  10  0
h  10
h  13
Distance
cannot be
negative!
The height is 10 cm.
Solve by factoring.
Example 1
–10
x2  3x  10
2
x2  3x  10  0 –5
–3
x  5x  2  0
x  5  0 or x  2  0
x  2
x5
Example 2
18
x2  9x  18  2x
–9 –2
x2  11x  18  0
–11
x  9x  2  0
x  9  0 or x  2  0
x 2
x9
Example 3 Find two consecutive integers x and x + 1
with a product of 110.
Example 4 A triangle has an area of 48 square inches.
Find the height, h, of the triangle if the base is (2h + 4)
inches.
Write in standard form before factoring.
Example 3 Find two consecutive integers x and x + 1
with a product of 110.
x  x  1  110
-110
x2  x  110
x2  x  110  0 11 -10
1
x  11x  10   0
x  11  0 or x  10  0
x  10
x  11
The numbers are -11 and -10,
or the numbers are 10 and 11.
Write in standard form before factoring.
Example 4 A triangle has an area of 48 square inches.
Find the height, h, of the triangle if the base is (2h + 4)
inches.
1
A  bh
2
1
48  2h  4 h
2
48  h  2h
-48
2
48  h  2h
8 -6
0  h2  2h  48
2
0  h  8h  6
h  8  0 or h  6  0
h6
h  8
Distance
cannot be
negative!
The height is 6 inches.
Practice: Solve by factoring.
1) x2  4x  3  0
 1,  3
2) x2  5x  4  0
1, 4
3) x2  5x  6  0
6,  1
4) x2  x  6  0
 3, 2
5) x2  5x  6  0
 2,  3
6) x2  4x  4  0
2
7) x2  3x  10  0
5,  2
8) x2  2x  8  0
 4, 2
Solve.
1) x  5x  6  0
 1, 6
2) x2  20  8x
 10, 2
3) x2  4x  6  3x
 1,  6
4) x2  7 x  22  3
3, 4
5) x2  x  7  7 x
7,  1
6) x2  13x  14
14,  1
7) x2  5x  6  0
 2,  3
8) x2  4x  4
2
2
Solve.
9) x2  10  3x
 2, 5
10) x2  2x  6  2
 4, 2
11) x2  3x  7  5x
 7,  1
12) xx  8  7
1, 7
13) x2  6x  6  7 x  20
 1, 14
14) xx  3  5  5x  52
 10, 2
15) x2  7 x  6
 1,  6
16) 3x2  4x  2x2  3x  12
3, 4
8-A6 Pages 437-438 # 11-32.