For the partially complete factorization, find the other binomial which will complete the factorization.
p^2+5p−14=(p−2)(_____)
To find the missing binomial, we need to determine what binomial, when multiplied by (p-2), will result in p^2+5p-14.
We can expand (p-2)(_____) using the distributive property:
(p-2)(_____) = p * _____ + (-2) * _____
Comparing this to p^2+5p-14, we can see that the first term in the binomial should be p and the second term should be positive.
Therefore, the other binomial which will complete the factorization is (p+7), because:
(p-2)(p+7) = p * p + (-2) * 7 = p^2 + 5p - 14