Factoring Polynomials 2

Characteristic Trinomials

To factor `x^2+px+q` find two numbers a e b, whose sum is p, a+b=p, and whose product is q, a * b=q. Then
`x^2+px+q=(x+a)(x+b)`
Examples:
1) `x^2+x-12`; you may want to write down a list of the different ways of factoring -12 as the product of two numbers:

1, -12; -1, 12; 2, -6; -2, 6; 3, -4; -3, 4;

Those factors are -3 and 4 because:
4 +(– 3) = 1
4 * (-3)= -12
we have: `x^2+x-12=(x+4)(x-3)`
2) `x^2+9x+20`, Those factor are 4 and 5 because
4 + 5 = 9
4 * 5 = 20
then `x^2+9x+20=(x+4)(x+5)`

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