Factoring Quadratic Equations -- Splitting the Middle Term

Is there a good way to always know how to split the middle term of a quadratic equation like x^2-9x+20=0?

It turns out that -5x and -4x "works" but is there a better way to split the term that is less tedious?

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Originally Posted by happyface

Is there a good way to always know how to split the middle term of a quadratic equation like x^2-9x+20=0?
It turns out that -5x and -4x "works" but is there a better way to split the term that is less tedious?

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Note that the constant term is , that means the two factors must have the same sign. But it must be because the middle term is negative. So what are they?

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Originally Posted by Plato

Note that the constant term is , that means the two factors must have the same sign. But it must be because the middle term is negative. So what are they?

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I see! Negative 4 and 5 equal 9 when added, and 20 when multiplied.

There are a few cases (like ax^2 + bx + c) where it is not so obvious where to split the middle term. That is especially where I get stumped, since c does not always equal the product of the "split" term.

Thats actually what I meant to ask about.

Quote:

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Originally Posted by happyface

I see! Negative 4 and 5 equal 9 when added, and 20 when multiplied. There are a few cases (like ax^2 + bx + c) where it is not so obvious where to split the middle term. That is especially where I get stumped, since c does not always equal the product of the "split" term.

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BUT is the product and is the sum.

Thanks! Very helpful.