# Class Notes 9-4 P

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```							                                                    Class Notes 9-4 P. 495

Essential Question:      How are polynomials factored and
how is the Zero Product Property
used to solve equations?

For trinomials of the form x^2 + bx +c, the coefficient of x^2 is 1. To
factor trinomials of this form, you find the factors of c whose sum is b.
This approach can be modified to factor trinomials whose leading
coefficient is not 1.

Apply the FOIL Method to the following:

(2x + 5)(3x + 1)

Observe the following pattern in this product:

You can use this pattern and the method of factoring by grouping to
factor 6x^2 + 17x + 5. Find two numbers, m and n whose product is 6 *
5 or 30 and whose sum is 17.

Factors of 30 Sum of Factors

6x^2 + 17x + 5 =

1
Factor ax^2 + bx + c

Factor 7x^2 + 22x + 3.

a = ______ b = _______c = ________

Sum = ________ Product = _________

Factor 10x^2 – 43x + 28.

a = ______ b = _______c = ________

Sum = ________ Product = _________

Sometimes the terms of a trinomial will contain a common factor. In
these cases, first use the Distributive Property to factor out the common
factor. Then factor the trinomial.

Factor When a, b, and c Have a Common Factor

Factor 3x^2 + 24x = 45.

a = ______ b = _______c = ________

Sum = ________ Product = _________

2
A polynomial that cannot be written as a product of two polynomials
with integral coefficients is called a prime polynomial.

Determine Whether a Polynomial is Prime

Factor 2x^2 +5x -2.

a = ______ b = _______c = ________

Sum = ________ Product = _________

Some equations of the form ax^2 + bx + c = 0 can be solved by factoring
and then using the Zero Product Property.

Solve Equations by Factoring

Solve 8a^2 – 9a – 5 = 4 – 3a. Check your solutions.

Steps
 Rewrite so that one side equals 0.
 Factor the left side.
 Apply the Zero Product Property.
 Solve each equation.
 Check.

A model for the vertical motion of a projected object is given by the
equation h = -16t^2 + vt + s, where h is the height in feet, t is the time in
seconds, v is the initial upward velocity in feet per second, and s is the
starting height of the object.

3
Solve Real-World Problems by Factoring

At a pep rally, small foam footballs are launched by cheerleaders using
a sling-shot. How long is a football in the air if a student in the stands
catches it on its way down 26 feet above the gym floor? Use the model
for vertical motion.

h = 16t^2 + vt + s

h = ______ t = _______ v = ______ s = _______

Your Turn

1. Factor 24x^2 – 22x + 3.

2. Factor 4x^2 + 24x + 32.

4
3. Factor 3x^2 + 7x – 5.

4. Solve 18b^2 – 19b – 8 = 3b^2 – 5b.

5. Ms. Smith’s science class built an air-launched model rocket for a
competition. When they test-launched their rocket outside the
classroom, the rocket landed in a nearby tree. If the launch pad was 2
feet off the ground, the initial velocity of the rocket was 64 feet per
second, and the rocket landed 30 feet above the ground, how long was
the rocket in flight? Use the equation h = 16t^2 + vt + s.

h = ______ t = _______ v = ______ s = _______

5

```
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