Factor 5x^2-11x+6

$5 x^{2} - 11 x + 6$

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 $a \cdot c = 5 \cdot 6 = 30$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$5 x^{2} - 11 (x) + 6$

Rewrite $- 11$ as $- 5$ plus $- 6$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$5 x (x - 1) - 6 (x - 1)$

Step 3

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

$(x - 1) (5 x - 6)$

Factor 5x^2-11x+6

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