5.3 Solve x2 + bx + c By Factoring
Monomial:
Binomial:
Trinomial:
Factoring Trinomials
m + n = b and mn = c
Factor the expression:
x2 + 5x + 6
x2 – 6x + 8
1
Factor x2 + bx + c when c is negative
Factor the expression:
x2 + 2x – 8 x2 ­ 2x ­ 15
Practice
Factor the expression:
1)
x2 + 6x + 5
2)
b2 + 7b + 12
3)
s2 – 5s + 4
4)
y2 + 11y – 12
5)
x2 + x – 6
6)
x2 – 15x ­ 16
2
Zero Product Property
• We can use factoring to solve and graph quadratic equations. • The solutions of a quadratic equation are called the roots.
• We find the roots using the zero product property.
(x + 5) (x + 2) = 0
Practice: Solve the equation
1.
(b + 2)(b + 4) = 0
2.
(x – 5)(x + 1) = 0
3.
x2 + 6x + 9 = 0
4.
x2 + 9x – 22 = 0
5.
x2 ­13x = ­ 42
6.
x2 + 10x = ­16
3
Use a quadratic as a model
A group of students from your school volunteer to build a neighborhood playground. The playground will have a mulch border along two sides. The mulch border will have the same width on both sides. The playground is a rectangle. The length of the playground is 20 yards and the width is 10 yards. There is enough mulch to cover 64 square yards for the border. How wide should the border be?
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HOMEWORK
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