Factoring Question

**cantstop01** · April 23rd 2010, 02:31 PM

I am asked to factor the equation

$4x^2 - 4x - 15 = 0$

To my knowledge, your supposed to find pairs of factors that multiply to give -15 and add to give -4, correct?

I can't find a pair that gives both those answers.

I'm stuck.

**skeeter** · April 23rd 2010, 02:38 PM

Originally Posted by cantstop01

I am asked to factor the equation

$4x^2 - 4x - 15 = 0$

To my knowledge, your supposed to find pairs of factors that multiply to give -15 and add to give -4, correct?

I can't find a pair that gives both those answers.

I'm stuck.

$4x^2 - 4x - 15 = (2x-5)(2x+3)$

**cantstop01** · April 23rd 2010, 02:55 PM

Thanks, looks like the answer is $x = 5/2$ and $x = -3/2$

I would like to ask one more thing.

what is the reasoning behind the factors not actually adding up to -4, yet still being the correct answer?

**skeeter** · April 23rd 2010, 03:12 PM

Originally Posted by cantstop01

Thanks, looks like the answer is $x = 5/2$ and $x = -3/2$

I would like to ask one more thing.

what is the reasoning behind the factors not actually adding up to -4, yet still being the correct answer?

that "technique" only works if the coefficient of $x^2$ is 1

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