Factor 3x^2-x-24

$3 x^{2} - x - 24$

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 24 = - 72$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- x$ .

$3 x^{2} - (x) - 24$

Rewrite $- 1$ as $8$ plus $- 9$

$3 x^{2} + (8 - 9) x - 24$

Apply the distributive property.

$3 x^{2} + 8 x - 9 x - 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 8 x) - 9 x - 24$

Factor out the greatest common factor (GCF) from each group.

$x (3 x + 8) - 3 (3 x + 8)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 8$ .

$(3 x + 8) (x - 3)$

Factor 3x^2-x-24

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