Question

Factor completely: 3x2 − 17x − 28

Answer 1

You can factor this by grouping.

3*-28 = -84
we need factors of -84 that sum to -17
2*42, 3*28, 4*21, 6*14, 7*12 are the factors of 84 if we just need two numbers. Can you see a pair of them that would give you -17 when added if the smaller number is positive and the larger number is negative?

After you've made your choice, you'll rewrite the equation as

\[3x^2 + ax - bx - 28\] where a is the smaller number and b is the larger number
Then group it like this:
\[(3x^2 + ax) - (bx + 28)\]
And you'll be able to factor the left hand term into
\[x(3x + a) - (bx + 28)\]and the right hand term will have a numeric factor you can take out as well. That will give you\[x(3x+a) - C(3x+a)\] and we can rewrite that as \[(3x+a)(x-C)\]which is our factored equation.