# Algebra factoring question: Why is the answer D? I don’t understand how they got there?

### 1 Answer

Relevance

- Roger the MoleLv 73 weeks ago
Substitute mn for p in each of the proposed answers, then look for counterexamples:

(A)

m + p = m + mn = m (1 + n)

When m = 2 and n = 3, the expression is = 8, and n is not a factor of 8

(B)

m + n + p = m + n + mn = m + n (1 + m)

When m = 2 and n = 3, the expression is = 11, and n is not a factor of 11

(C)

mp - m = nm^2 - m = m (mn - 1)

When m = 2 and n = 3 , the expression is = 10, and n is not a factor of 10

(D)

mp - n = m^2n - n = n (m^2 - 1)

n is always a factor of n (m^2 - 1) except when m = 1

(E)

np - m = mn^2 - m = m (n^2 -1)

When m = 2 and n = 3, the expression is = 16, and n is not a factor of 16

So the answer closest to correct is (D).

[(D) could be made entirely correct by adding the requirement: m > n ]

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