Factor 3n^2-8n+4

$3 n^{2} - 8 n + 4$

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 $a \cdot c = 3 \cdot 4 = 12$ and whose sum is $b = - 8$ .

Factor $- 8$ out of $- 8 n$ .

$3 n^{2} - 8 (n) + 4$

Rewrite $- 8$ as $- 2$ plus $- 6$

$3 n^{2} + (- 2 - 6) n + 4$

Apply the distributive property.

$3 n^{2} - 2 n - 6 n + 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 n^{2} - 2 n) - 6 n + 4$

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

$n (3 n - 2) - 2 (3 n - 2)$

Step 3

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

$(3 n - 2) (n - 2)$

Factor 3n^2-8n+4

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