Factor 4x^2+27x+35

$4 x^{2} + 27 x + 35$

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 $b = 27$ .

Factor $27$ out of $27 x$ .

$4 x^{2} + 27 (x) + 35$

Rewrite $27$ as $7$ plus $20$

$4 x^{2} + (7 + 20) x + 35$

Apply the distributive property.

$4 x^{2} + 7 x + 20 x + 35$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 7 x) + 20 x + 35$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 7$ .

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

Factor 4x^2+27x+35

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