Factor 4x^2+23x-35

$4 x^{2} + 23 x - 35$

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 $a \cdot c = 4 \cdot - 35 = - 140$ and whose sum is $b = 23$ .

Factor $23$ out of $23 x$ .

$4 x^{2} + 23 (x) - 35$

Rewrite $23$ as $- 5$ plus $28$

$4 x^{2} + (- 5 + 28) x - 35$

Apply the distributive property.

$4 x^{2} - 5 x + 28 x - 35$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 5 x) + 28 x - 35$

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

$x (4 x - 5) + 7 (4 x - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 5$ .

$(4 x - 5) (x + 7)$

Factor 4x^2+23x-35

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