Factor 14x^2-53x+14

$14 x^{2} - 53 x + 14$

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 $a \cdot c = 14 \cdot 14 = 196$ and whose sum is $b = - 53$ .

Factor $- 53$ out of $- 53 x$ .

$14 x^{2} - 53 (x) + 14$

Rewrite $- 53$ as $- 4$ plus $- 49$

$14 x^{2} + (- 4 - 49) x + 14$

Apply the distributive property.

$14 x^{2} - 4 x - 49 x + 14$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 x^{2} - 4 x) - 49 x + 14$

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

$2 x (7 x - 2) - 7 (7 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 2$ .

$(7 x - 2) (2 x - 7)$

Factor 14x^2-53x+14

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