Factor 4x^2+x-18

$4 x^{2} + x - 18$

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 $a \cdot c = 4 \cdot - 18 = - 72$ and whose sum is $b = 1$ .

Multiply by $1$ .

$4 x^{2} + 1 x - 18$

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

$4 x^{2} + (- 8 + 9) x - 18$

Apply the distributive property.

$4 x^{2} - 8 x + 9 x - 18$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 8 x) + 9 x - 18$

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

$4 x (x - 2) + 9 (x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 2$ .

$(x - 2) (4 x + 9)$

Factor 4x^2+x-18

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