Page 119 - Math Course 2 (Book 1)

Factoring: Polynomials

MO. 4 - L1b
Let’s Begin
Solving Equations of the Form

ax2 + bx = 0
Solve an Equation
Vocabulary A-Z
Let us learn some vocabulary Examples

Solve (x – 2)(4x – 1) = 0. Check the solution.
Zero Products Property If (x – 2)(4x – 1) = 0, then according to the Zero
Product Property, either x – 2 = 0 or 4x – 1 = 0.
The Zero Product Property simply states that if
ab = 0, then either a = 0 or b = 0 (or both). A product (x – 2)(4x – 1) = 0 Original equation
of factors is zero if and only if one or more of the
factors is zero. x – 2 = 0 or 4x – 1 = 0 Set each factor equal to
ab = 0 zero.
a = 0, b = 0
x = 2 4x = 1 Solve each equation.
6(0) = 0 0(3) = 0 x = 1
(5 – 5) (0) = 0 –2(–3 + 3) = 0 4
Roots Answer The roots are 2 and 1
4
The solutions of an equation are called the roots of
the equation. Check 1
Substitute 2 and for x in the original equation.
4
(d – 5)(3d + 4) = 0
If (d – 5)(3d + 4) = 0, then according to the (x – 2)(4x – 1) = 0 (x – 2)(4x – 1) = 0
?
?
Zero Product Property either d – 5 = 0 or (2 – 2)(4 • 2 – 1) = 0 –2 4 • –1 = 0
1
1
3d + 4 = 0 4 4
? 7 ?
(0) (7) = 0 – (0) = 0
(d – 5)(3d + 4) = 0 Original Equation 4
0 = 0 0 = 0
d – 5 = 0 or 3d + 4 = 0 Set each factor
2
equal to zero. Solve 4y = 12y . Check the solution.
Write the equation so that it is of the form ab = 0.
d = 5 3d = –4 Solve each
equation.
2
3 4y = 12y Original equation
d = –
4 2 2
3
The roots are 5 and – . 4y – 12y = 0 Subtract 12y from each side.
4
4y(1 – 3y) = 0 Factor the GCF of 4y and
2
Key Concept 12y , which is 4y.
4y = 0 or 1 – 3y = 0 Zero Product Property

Zero Product Property –3y = –1

1
Words If the product of two factors is 0, then at y = 0 y = 3
least one of the factors must be 0.
1
The roots are 0 and .
Symbols For any real numbers a and b, if ab = 0, 3 1
3
then either a = 0, b = 0, or both a and b Answer Check by substituting 0 and
equal zero. for y in the original equation.
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