Factor by Grouping 4x^2+5x-6

$4 x^{2} + 5 x - 6$

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 $a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is $b = 5$ .

Factor $5$ out of $5 x$ .

$4 x^{2} + 5 (x) - 6$

Rewrite $5$ as $- 3$ plus $8$

$4 x^{2} + (- 3 + 8) x - 6$

Apply the distributive property.

$4 x^{2} - 3 x + 8 x - 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 3 x) + 8 x - 6$

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

$x (4 x - 3) + 2 (4 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 3$ .

$(4 x - 3) (x + 2)$

Factor by Grouping 4x^2+5x-6

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