Factoring Polynomials of the form ax2 bx c

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10.6
Factoring Polynomials of the form ax2 bx c
Goal Factor Polynomials whose lead
coefficient is other than 1
2
 
The GCF for a polynomial is the largest monomial
that divides (is a factor of) each term of the
polynomial.
 
   
Step 1  Identify the GCF of the polynomial.
Step 2   Divide the GCF out of every term of the
polynomial.
     
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Review Factor the trinomial
2y(x 5)(x 3)
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Again, this is the reverse of the FOIL method.
The difference between this trinomial and the
one discussed above, is there is a number other
than 1 in front of the x2.  This means, that not
only do you need to find factors of c, but also
a.
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Step 2 Use trial and error to find the factors
needed.
The factors of a will go in the first terms of
the binomials and the factors of c will go in the
last terms of the binomials. 
The trick is to get the right combination of
these factors.  You can check this by applying
the FOIL method.  If your product comes out to be
the trinomial you started with, you have the
right combination of factors.  If the product
does not come out to be the given trinomial, then
you need to try again.

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Factor the trinomial 
Note that this trinomial does not have a GCF. 
So we go right into factoring the trinomial of
the form
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Step 2 Use trial and error to find the factors
needed.
In the first terms of the binomials, we need
factors of 3x2 . This would have to be 3x and
x.
In the second terms of the binomials, we need
factors of 2.  This would have to be 2 and 1. 
Also, we need to make sure that we get the right
combination of these factors so that when we
multiply them out we get  3x2 5x 2.
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Factor the trinomial
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Factor the trinomials
9x2 65x 14 4x2 13x 10
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Factor the trinomials
6x2 23x 15 8x2 38x 9
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Solve by factoring the trinomials
2x2 7x 3 0 5n2 17n -6
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Homework
p. 614, 16-62 evens