Find a factor of 3x^2- 4x - 7

3x^2 - 4x - 7

1. Split the second term in 3x^2 - 4x - 7 into two terms.
3x^2 + 3x - 7x - 7

1. Multiply the coefficient of the first terms by the constant term.
3 * - 7 = -21

2. Ask: Which two numbers add up to -4 and multiply to -21?
3 and -7

3. Split -4x as the sum of 3x and -7x.
3x^2 + 3x - 7x - 7

2. Factor out the common terms in the first two terms, then in the last two terms.
3x(x+1) - 7(x + 1)

3. Factor out the common term x + 1.
(x + 1)(3x - 7)

So therefore your answer is:

(x + 1)(3x - 7)

What’s the improper fraction?