Factor 4x^2-23x+15

$4 x^{2} - 23 x + 15$

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 $a \cdot c = 4 \cdot 15 = 60$ and whose sum is $b = - 23$ .

Factor $- 23$ out of $- 23 x$ .

$4 x^{2} - 23 (x) + 15$

Rewrite $- 23$ as $- 3$ plus $- 20$

$4 x^{2} + (- 3 - 20) x + 15$

Apply the distributive property.

$4 x^{2} - 3 x - 20 x + 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 3 x) - 20 x + 15$

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

$x (4 x - 3) - 5 (4 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 3$ .

$(4 x - 3) (x - 5)$

Factor 4x^2-23x+15

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