Factor by Grouping 14x^2+x-4

$14 x^{2} + x - 4$

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 $a \cdot c = 14 \cdot - 4 = - 56$ and whose sum is $b = 1$ .

Multiply by $1$ .

$14 x^{2} + 1 x - 4$

Rewrite $1$ as $- 7$ plus $8$

$14 x^{2} + (- 7 + 8) x - 4$

Apply the distributive property.

$14 x^{2} - 7 x + 8 x - 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 7 x) + 8 x - 4$

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

$7 x (2 x - 1) + 4 (2 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 1$ .

$(2 x - 1) (7 x + 4)$

Factor by Grouping 14x^2+x-4

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