# Find the prime factorization of the polynomial. 2t^{2}-4t-48

Find the prime factorization of the polynomial.
$2{t}^{2}-4t-48$
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Ben Owens
Step 1
Given polynomial
$p\left(t\right)=2{t}^{2}-4t-48$...(i)
eq i is ab the form $a{t}^{2}+bt+c$
To find prime factorization multiply "a" and "c" and then write factor for "ac", so that it will add up to "b"
Step 2
$\therefore 2×-48=-96$
$=-12×8$
$\therefore$ eq i can be written as
$p\left(t\right)=2{t}^{2}-12t+8t-48$
=2t(t-6)+8(t-6)
p(t)=(t-6)(2t+8)