Factor 6x^2-25x+4

$6 x^{2} - 25 x + 4$

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 $a \cdot c = 6 \cdot 4 = 24$ and whose sum is $b = - 25$ .

Factor $- 25$ out of $- 25 x$ .

$6 x^{2} - 25 (x) + 4$

Rewrite $- 25$ as $- 1$ plus $- 24$

$6 x^{2} + (- 1 - 24) x + 4$

Apply the distributive property.

$6 x^{2} - 1 x - 24 x + 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} - 1 x) - 24 x + 4$

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

$x (6 x - 1) - 4 (6 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x - 1$ .

$(6 x - 1) (x - 4)$

Factor 6x^2-25x+4

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