Question

For the partially complete factorization, find the other binomial which will complete the factorization.

a²−12a+ 32=(a−8)(_____)

Answer 1

The other binomial that completes the factorization of a²−12a+32 is (a-4), making the fully factored form (a-8)(a-4).

Step-by-step explanation:

To complete the factorization of the quadratic expression a²−12a+32, we already have one binomial (a-8). To find the other binomial, we need a number that when added to -8 gives -12 (the coefficient of the middle term) and when multiplied by -8 gives 32 (the constant term).

By trial and error or by knowledge of factor pairs of 32, we find that 4 fits these criteria since (-8)+4=-4, which will replace the middle term -12a when the binomials are multiplied, and (-8)×4=32.

Therefore, the other binomial that completes the factorization is (a-4).

So the fully factored form of a²−12a+32 is (a-8)(a-4).