Factoring quadratics.notebook
May 11, 2015
Goals:
* Factor polynomials.
* Use zero­product property to solve quadratic
equations.
* Use the quadratic formula to solve quadratic
equations.
* Use zeros and symmetry to sketch a graph of a quadratic function.
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Factoring quadratics.notebook
May 11, 2015
Multiply.
1.
2.
3.
4.
5.
6.
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Factoring quadratics.notebook
May 11, 2015
To factor a polynomial means to express the polynomial as
a product of two or more polynomials.
For quadratic polynomials, we have three cases:
Quadratic trinomial
.
factors
linear binomial times linear binomial
( )( )
or
GCF( )( )
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Factoring quadratics.notebook
May 11, 2015
Quadratic Binomial where "linear" term is missing, ie 0x
rs
facto
If "a" is a perfect square and "c" is the opposite of a perfect square so we have then difference of squares: binomial times binomial
or factor out a common factor of
a and c.
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Factoring quadratics.notebook
May 11, 2015
Quadratic Binomial where "constant" term is missing.
factors
monomial times binomial
____ ( )
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Factoring quadratics.notebook
May 11, 2015
Steps for factoring
1. Factor out the greatest common factor.
* Look for factors of coefficients and variables common
to all the terms. Use distributive property to factor.
* If the leading coefficient is negative, it may be helpful
to factor out a negative 1 (along with any other common factors).
2. Use the form of the polynomial to help you decide what to do:
* Trinomial factors into two binomials
* Binomial Difference of squares (linear term is zero) factors into two binomials
If the constant term is zero, factor into a monomial (GCF) and binomial.
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Factoring quadratics.notebook
May 11, 2015
The graph is a parabola.
Zeros when If zeros are real, then the zeros are the x­axis
intercepts.
The x­coordinate of the vertex is the midpoint of the
zeros.
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Factoring quadratics.notebook
May 11, 2015
If the quadratic is in polynomial form, sometimes it's
easier to find the zeros using the Zero Product Property.
Zero Product Property
If the product of two (or more) numbers is zero, then: at least one of the numbers is zero.
Algebraically: If ab = 0, then a = 0 or b = 0.
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Factoring quadratics.notebook
May 11, 2015
Determine the zeros using the Zero Product Property
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Factoring quadratics.notebook
May 11, 2015
Determine the zeros using the Zero Product property
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Factoring quadratics.notebook
May 11, 2015
What if the quadratic is irreducible over the polynomials
with rational coefficients? How do we find the zeros then?
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Factoring quadratics.notebook
May 11, 2015
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