Factoring Polynomials

Question

Y²-17y+72

Answer 1

A trinomial, if factorable, will factor into the product of two binomials. The method to factor this one is fairly straight forward since the coefficient of the first term is 1. We are essentially "undoing" the result of FOIL'ing.

(a + b)(a + b) = a² + 2ab + b²

First thing to do is just set up some brackets.

(            )(            )

Now, the first term in the trinomial (y²) can be factored into

(y          )(y           )  Don't worry about signs at this point

Now we ask ourselves this question, what two factors multiply to give the constant term (72) but sum to give the coefficient of the middle term (-17)?

List factors of 72

1       72
2       36
3       24
4       18
6       12
8        9

(y      8)(y       9)

You see that 8 and 9 multiply to give 72, but what do their signs have to be in order to sum to -17? Both would have to be negative.

(y - 8)(y - 9) FOIL to check ==> y² - 9y - 8y + 72 = y² - 17y + 72