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Algebra 2
4-6 Factoring Quadratic Polynomials
4-6 Factoring Quadratic Polynomials
WARMUP
Factor:
3
2
1
6 9
y
z z
4-6 Factoring Quadratic Polynomials
Recall:
Perfect Square Trinomials:
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Difference of Squares:
a2 – b2 = (a + b)(a – b)
4-6 Factoring Quadratic Polynomials
AND:
Sum and Differences of Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
a3 – b3 = (a – b)(a2 + ab + b2)
4-6 Factoring Quadratic Polynomials
a3 – b3 = (a – b)(a2 + ab + b2)
3
3 3
2
1
1
( 1)( 1)
y
y
y y y
4-6 Factoring Quadratic Polynomials
a2 + 2ab + b2 = (a + b)2
2
2 2
6 9
2 3 3
z z
z z
4-6 Factoring Quadratic Polynomials
Polynomials of the form:
ax2 + bx + c ( a0 )
Are called quadratic (from quadratus in Latin, which means square) or second degree polynomials.
ax2 is the quadratic term
bx is the linear term
c is the constant term.
4-6 Factoring Quadratic Polynomials
A quadratic trinomial is a quadratic polynomial for which a, b, and c are all nonzero integers.
The previous examples that we looked at were forms of perfect squares or cubes. Now we’ll factor quadratic trinomials that are not necessarily perfect squares…
4-6 Factoring Quadratic Polynomials
If ax2 + bx + c can be factored into the product (px+q)(rx+s) where p, q, r, s are integers, then:
ax2 + bx + c = (px+q)(rx+s)
= prx2 + (ps + qr)x + qs
SO:
a = pr b = ps + qr c = qs
4-6 Factoring Quadratic Polynomials
What does all that mean?
Let’s look at example 1, p. 188
4-6 Factoring Quadratic Polynomials
More examples
4-6 Factoring Quadratic Polynomials
How about
x2 + 4x - 3
4-6 Factoring Quadratic Polynomials
4-6 Factoring Quadratic Polynomials
4-6 Factoring Quadratic Polynomials
4-6 Factoring Quadratic Polynomials
4-6 Factoring Quadratic Polynomials