Lesson M871  Factoring Type 1 Polynomials  1
When we multiply two polynomials together we can write the product in expanded
form. If we were to write an expanded polynomial as the product of two (or
more) polynomials, we would be putting the polynomial into factored form.
factored form > (x + 2)(x + 3) = x^{2}+5x +
6 < expanded form
To factor means to rewrite a polynomial as a product of
polynomials. In the above example (x + 2) and (x + 3) are the factors
of (x^{2}+ 5x + 6).
How do we factor a trinomial like x^{2}+7x + 12?
Recall our general expansion:
(x + a)(x + b) = x^{2 }+ (a + b)x + ab
The sum of a and b gives us the coefficient of the x term
and the product of a and b gives us the constant term.
In the example x^{2}+7x + 12 we need to find two numbers such that their
sum is +7 and their product is +12.
Start by listing the factors of 12 in a chart, along with the sum of the
factors.
Factors

Sum

1, 12

13

2, 6

8

3, 4

7

3, 4

7

2, 6

8

1, 12

13

We can see from the chart that the only pair of numbers that have a product or
+12 and a sum of +7 are 3 and 4.
Thus we can factor as follows:
x^{2}+ 7x + 12 = (x + 3)(x + 4)
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