Factor 5x^2-12x+4

$5 x^{2} - 12 x + 4$

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 $a \cdot c = 5 \cdot 4 = 20$ and whose sum is $b = - 12$ .

Factor $- 12$ out of $- 12 x$ .

$5 x^{2} - 12 (x) + 4$

Rewrite $- 12$ as $- 2$ plus $- 10$

$5 x^{2} + (- 2 - 10) x + 4$

Apply the distributive property.

$5 x^{2} - 2 x - 10 x + 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 2 x) - 10 x + 4$

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

$x (5 x - 2) - 2 (5 x - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

$(5 x - 2) (x - 2)$

Factor 5x^2-12x+4

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