Factor 5x^2+x-6

$5 x^{2} + x - 6$

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 $a \cdot c = 5 \cdot - 6 = - 30$ and whose sum is $b = 1$ .

Multiply by $1$ .

$5 x^{2} + 1 x - 6$

Rewrite $1$ as $- 5$ plus $6$

$5 x^{2} + (- 5 + 6) x - 6$

Apply the distributive property.

$5 x^{2} - 5 x + 6 x - 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 5 x) + 6 x - 6$

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

$5 x (x - 1) + 6 (x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$(x - 1) (5 x + 6)$

Factor 5x^2+x-6

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