Question

# Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary: 6a^{2}-48a-120

Polynomial factorization
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
$$6a^{2}-48a-120$$

2021-05-15
Step 1
Greatest common factor of a polynomial is the factor that is present in all terms of the polynomial. First check the coefficients of the polynomial to find constant greatest factor and then check all the variable terms to check the greatest common variable term. Then multiply both to get the greatest common factor.
Step 2
The given polynomial equation is $$6a^{2}-48a-120$$. First find the greatest common constant present in the polynomial by checking all coefficients.
$$6a^{2}-48a-120=6a^{2}-6\times 8a-6\times 20$$
$$=6(a^{2}-8a-20)$$
From this it can be seen that 6 is the greatest common constant. Now check the variable terms. As the polynomial contains a constant term -120, so all terms doesn't contain a variable. so, the greatest common variable is 1.
Hence, the greatest common factor of a given polynomial is constant 6.
Simplify the given polynomial as factors as follows.
$$6a^{2}-48a-120=6(a^{2}-8a-20)$$
$$=6(a^{2}+2a-10a-20)$$
=6(a(a+2)-10(a+2))
=6(a-10)(a+2)
Hence, the greatest common factor of a given polynomial is constant 6 and the polynomial can be factored as $$6a^{2}-48a-120=6(a-10)(a+2)$$.