algebra 2 4-6 factoring quadratic polynomials. warmup factor:

Algebra 2

4-6 Factoring Quadratic Polynomials


WARMUP

Factor:

3

2

1

6 9

y

z z


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)


AND:

Sum and Differences of Cubes

a3 + b3 = (a + b)(a2 – ab + b2)

a3 – b3 = (a – b)(a2 + ab + b2)


a3 – b3 = (a – b)(a2 + ab + b2)

3

3 3

2

1

1

( 1)( 1)

y

y

y y y


a2 + 2ab + b2 = (a + b)2

2

2 2

6 9

2 3 3

z z

z z


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.


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…


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


What does all that mean?

Let’s look at example 1, p. 188


More examples


How about

x2 + 4x - 3

algebra 2 4-6 factoring quadratic polynomials. warmup factor:

Documents