Factor 3x^2-11x+8

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

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = - 11$ .

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

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$3 x (x - 1) - 8 (x - 1)$

Step 3

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

$(x - 1) (3 x - 8)$

Factor 3x^2-11x+8

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