Hi! So first thing we have to do is find the GCF of the terms.

This is the given data:

3a^3b + 18a^2b - 21ab

The GCF of these three terms are 3ab.

Divide each term by their GCF.

3a^3b / 3ab + 18a^2b / 3ab - 21 ab / 3ab

We have a quotient of:

a^2 + 6a - 7

This is an example of a Quadratic Trinomial.

We can factor it by finding the factors of the last term's coefficient that if multiplied, it is the coefficient itself and if added, it is the middle term's coefficient.

-7 = (1, -7) and (-1, 7)

We can use (-1 and 7) as it is the product of the last term's coefficient and the sum of the middle term's coefficient.

Make two parentheses.

()()

Square the first term (a^2) and put the result in each parenthesis.

(a)(a)

Now put the two factors earlier to get our final answer!

(a - 1)(a + 7)

Signature: Sora The QT <3