Factor 11x^2-8x-3

$11 x^{2} - 8 x - 3$

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 $a \cdot c = 11 \cdot - 3 = - 33$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 x$ .

$11 x^{2} - 8 (x) - 3$

Rewrite $- 8$ as $3$ plus $- 11$

$11 x^{2} + (3 - 11) x - 3$

Apply the distributive property.

$11 x^{2} + 3 x - 11 x - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(11 x^{2} + 3 x) - 11 x - 3$

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

$x (11 x + 3) - (11 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $11 x + 3$ .

$(11 x + 3) (x - 1)$

Factor 11x^2-8x-3

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