Download Cover in 1 day

Mr. Borosky
Section 9.6
Algebra 1
9.6 Factor ax2 + bx + c p. 593-599
Objective: 1. You will factor trinomials of the form ax2 + bx + c.
To Factor Trinomials of the form ax2 + bx + c means to write the
Trinomial as the Product of 2 Binomials (Factored Form).
One way to factor
ax2 + bx + c
is to find Numbers “p” and “r”
whose product is “a” and find Numbers “q” and “s” whose product is “c”
so that the middle term is the sum of the Outer and Inner Products of
FOIL.
******
ax2 + bx + c
=
where a
c
b
(px + q)(rx + s)
= pr
= qs
= ps + qr
In factoring trinomials of the form ax2 + bx + c you are finding 2 terms
that satisfy the following 2 conditions.
1. Their Product is the same as the product of the first & last
terms
2. Their Sum is the same as the middle term.
1. ax2 + bx + c
First:
Bring down ax2 Plus Sign, Parentheses, x, & c_
or
ax2 + (
)x _+ c___
Second: Multiply ac and find factors of ac
That add to give you b
Third:
_Distribute the variable(s) (get 4 terms)__
Fourth: _Group 4 Terms into 2 groups of 2
_Factor out common part in each group
_Find what is left (common binomial)
Fifth:
_Common Binomial is one Factor
what is left is the other factor
If a is negative factor out -1 first then fit it to the pattern
Roots – solutions of a quadratic equation.
(x-Intercepts).
9.6 Factor ax2 + bx + c p. 593-599
Where it crosses the x-axis
Page 1 of 2
Mr. Borosky
Section 9.6
Algebra 1
Zero Product Property – ab = 0 if and only if a = 0 or b = 0.
To use the Zero Product Property to solve a Polynomial Equation:
1. Write the equation with ZERO as one side
2. Factor the other side of the equation and
3. Solve the equation by setting each factor equal to Zero.
Zero of a Function – a number is a zero of a function if f(r) = 0.
example, 3 and –3 are zeros of g(x) = x2 – 9 since
g(3) = 32 – 9 = 9 – 9 = 0 and g(-3) = (-3)2 – 9 = 9 – 9 = 0
9.6 Factor ax2 + bx + c p. 593-599
Page 2 of 2
For