Question 424701: Factor the trinomial
w^2-13w+36
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Since the first term is w^2, both factors begin with just w. Since the last term is positive (+ 36), the factors will both be (w + _) or (w - _), because two positives multiply to be positive and two negatives multiply to be positive. Since the middle term is negative (- 13w), the factors will both be (w - _), because two negatives add to be negative, while two positives add to be positive. So now we need the two negative numbers that multiply to be 36 and add to be -13. Look at factors of 36. Factor pairs are: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. Which pair add to 13? 4 and 9. So the factors are (w - 4) and (w - 9). Remember, this is not usually as complicated as it seems, since most of this was just explanation.
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