Question 1094766: Please help with the following:
Factor: 2𝑥^2 + 11𝑥 + 15
Thank you! Found 2 solutions by ikleyn, Alan3354:Answer by ikleyn(52781) (Show Source):
Before making factoring, find the roots by using the quadratic formula:
= = .
= = = .
= = = -3.
It means that factoring has the form
= = (<<<---=== Notice that coef. 2 before the parentheses is the LEADING COEF-T of the polynomial;
(the numbers (-5/2) and (-3) are the roots that you found above)
= 2*(x+5/2)*(x+3)}}} = (2x+5)*(x+3),
and your task is completed.
Different people use different approaches. Some try to guess the coefficients of factoring.
My personal approach is: if I can not see the factors in 5 seconds, I use the quadratic formula.
You can put this solution on YOUR website! Factor: 2𝑥^2 + 11𝑥 + 15
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If you're not yet familiar with the quadratic equation, factoring is "trial & error"
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Note that all coefficients are positive.
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It has to be
(x + ?)*(2x + ?)
or
(x + a)*(2x + b)
a*b = 15
Try pairs of factors of 15
There are only 2 pair, 1*15 and 3*5
15 is greater than 11, so it's eliminated.
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So it's either
(x + 3)*(2x + 5)
or
(x + 5)*(2x + 3)
