Factor 3a^2-13a+4

$3 a^{2} - 13 a + 4$

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 $b = - 13$ .

Factor $- 13$ out of $- 13 a$ .

$3 a^{2} - 13 (a) + 4$

Rewrite $- 13$ as $- 1$ plus $- 12$

$3 a^{2} + (- 1 - 12) a + 4$

Apply the distributive property.

$3 a^{2} - 1 a - 12 a + 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 a^{2} - 1 a) - 12 a + 4$

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

$a (3 a - 1) - 4 (3 a - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 a - 1$ .

$(3 a - 1) (a - 4)$

Factor 3a^2-13a+4

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