Factor 4x^2-15x-4

$4 x^{2} - 15 x - 4$

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 $a \cdot c = 4 \cdot - 4 = - 16$ and whose sum is $b = - 15$ .

Factor $- 15$ out of $- 15 x$ .

$4 x^{2} - 15 (x) - 4$

Rewrite $- 15$ as $1$ plus $- 16$

$4 x^{2} + (1 - 16) x - 4$

Apply the distributive property.

$4 x^{2} + 1 x - 16 x - 4$

Multiply $x$ by $1$ .

$4 x^{2} + x - 16 x - 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + x) - 16 x - 4$

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

$x (4 x + 1) - 4 (4 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (x - 4)$

Factor 4x^2-15x-4

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