9.4
- Solving Polynomial Equations in Factored Form
I.
The Greatest Common Factor
A GCF, or Greatest Common Factor, is the largest monomial that divides
evenly into each term of a polynomial.
Let’s start by finding the GCF of the following numbers
and monomials:
1.
3 and 9
2. 2 and 11
3. 12 and 24
4.
8x and 20x
5. 4x
2
and 18x
6. 8y
5
, 30y
6
II.
Factoring out a GCF (Reverse of Distribution)
EXAMPLE:
3x(4x
5
+ 3)
multiplies
out to ____________
12x
6
+ 9x
factors
to ____________________
Factoring focuses on undoing multiplication.
We are dividing out the GCF.
Try factoring out the GCF of these polynomials:
1.
4x
2
+ 24x
3
2.
9 - 9a
3.
2
4
20
x
x
2.
8x+12y
5. 14y
2
+21
6.
c d
c d
2
4
3
7.
4
4
3
2
2
2
12
3
6
m n
m n
m n

III.The Zero-Product Property Recall the two different forms of polynomials, standard form and factored form. Standard Form: 2x2+ 7x –15 = 0 Factored Form: (2x –3)(x + 5) = 0 How can we solve for x in the following equations in factored form? a)(x –3)(x + 2) = 0 b) (x + 1)(x + 3) = 0 These x values are called ___________________________________________________________________. This property is called the Zero-Product Property. To use the ZPP, the polynomial must be in factored form and the equation must equal zero.
Let’s Practice:
1) (2x + 3)(x –4) = 0 2) 6x(x –4) = 0 The Zero-Product Property: If ab= 0, then _______________________.

3) (2x + 1)(3x –3)(x –5) = 0 4) x(y –8)(2y –9) = 0
IV.Try it! Factor and solve.
1.228xx2. 2615n
n