Factor 4x^2+27x-7

$4 x^{2} + 27 x - 7$

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 $a \cdot c = 4 \cdot - 7 = - 28$ and whose sum is $b = 27$ .

Factor $27$ out of $27 x$ .

$4 x^{2} + 27 (x) - 7$

Rewrite $27$ as $- 1$ plus $28$

$4 x^{2} + (- 1 + 28) x - 7$

Apply the distributive property.

$4 x^{2} - 1 x + 28 x - 7$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 1 x) + 28 x - 7$

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

$x (4 x - 1) + 7 (4 x - 1)$

Step 3

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

$(4 x - 1) (x + 7)$

Factor 4x^2+27x-7

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