Factor 6x^2-23x+21

$6 x^{2} - 23 x + 21$

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 $a \cdot c = 6 \cdot 21 = 126$ and whose sum is $b = - 23$ .

Factor $- 23$ out of $- 23 x$ .

$6 x^{2} - 23 (x) + 21$

Rewrite $- 23$ as $- 9$ plus $- 14$

$6 x^{2} + (- 9 - 14) x + 21$

Apply the distributive property.

$6 x^{2} - 9 x - 14 x + 21$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} - 9 x) - 14 x + 21$

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

$3 x (2 x - 3) - 7 (2 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (3 x - 7)$

Factor 6x^2-23x+21

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