SOLUTION: factor the trinomial using a binomial: 4x^2+24x+27

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Question 1025360: factor the trinomial using a binomial:
4x^2+24x+27
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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factor the trinomial using a binomial:
4x^2+24x+27
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1. Apply the quadratic formula to find the roots of the polynomial.

   The roots are 

   x%5B1%2C2%5D = %28-24+%2B-+sqrt%28%28-24%29%5E2+-+4%2A4%2A27%29%29%2F8 = %28-24+%2B-+sqrt%28144%29%29%2F8 = %28-24+%2B-+12%29%2F8.

   So, x%5B1%5D = -36%2F8 = -4.5  and  x%5B2%5D = -12%2F8 = -1.5.

2. Hence, the factorization is 

   4x%5E2%2B24x%2B27 = 4%2A%28x+-+x%5B1%5D%29%2A%28x+-+x%5B2%5D%29 = 4*(x - (-4.5))*(x - (-1.5)) = (2x + 9)*(2x + 3).

It is your answer.