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Mr. Borosky
Section 4.4
4.4 Solve ax2 + bx + c = 0 by Factoring p. 259-265
Algebra 2
Objective: 1. You will use factoring to solve quadratic equations 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.
Perfect
(a + b)
(a
(a
Square Trinomials – the Trinomials that result from squaring
or (a – b)
+ b)2 = a2 + 2ab + b2
– b)2 = a2 – 2ab + b2
To determine whether a trinomial can be factored in this way, first
decided if it is a perfect square. Can it be written in either form
(
(a + b)2 = a2 + 2ab + b2
or
(a – b)2 = a2 – 2ab + b2
)
Greatest Common Factor (GCF) – for integers, the greatest integer that
is a factor of each. Also, for monomials the common factor that has the
greatest degree and greatest numerical coefficient.
The GCF should always be factored out before factoring using the
patterns. Occasionally, factoring the difference of squares (or other
pattern) needs to be used more than once in a problem.
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.
4.4 Solve ax2 + bx + c = 0 by Factoring p. 259-265
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