x2+9x+20

s2-100

t2-3t-28

36m2-121

How do you factor

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- Jun 21st 2009, 11:10 AMLOLFactor each of the following
x2+9x+20

s2-100

t2-3t-28

36m2-121

How do you factor - Jun 21st 2009, 11:24 AMskeeter
- Jun 21st 2009, 01:53 PMyeongil
The first and third have a leading coefficient of 1. So you know that the first terms have to be

$\displaystyle x^2 + 9x + 20 = ({\color{red}x}\;+\;?)({\color{red}x}\;+\;?)$

To fill in the last terms, ask yourself, what are the factors of 20 whose sum is 9? It's +4 and +5, so fill them in:

$\displaystyle x^2 + 9x + 20 = (x\;+\;{\color{red}4})(x\;+\;{\color{red}5})$

The second and fourth are one of the special patterns that you should memorize -- these involve difference of two squares. The pattern is

$\displaystyle a^2 - b^2 = (a + b)(a - b)$

a would correspond to s, and b would correspond to 10:

$\displaystyle s^2 - 100 = s^2 - 10^2 = (s\;+\;10)(s\;-\;10)$

I'll let you try the other two.

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