Factor 9-16x+7x^2

$9 - 16 x + 7 x^{2}$

Step 1

Reorder terms.

$7 x^{2} - 16 x + 9$

Step 2

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 $a \cdot c = 7 \cdot 9 = 63$ and whose sum is $b = - 16$ .

Factor $- 16$ out of $- 16 x$ .

$7 x^{2} - 16 (x) + 9$

Rewrite $- 16$ as $- 7$ plus $- 9$

$7 x^{2} + (- 7 - 9) x + 9$

Apply the distributive property.

$7 x^{2} - 7 x - 9 x + 9$

Step 3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 7 x) - 9 x + 9$

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

$7 x (x - 1) - 9 (x - 1)$

Step 4

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

$(x - 1) (7 x - 9)$

Factor 9-16x+7x^2

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