Factor 4x^2+13x+10

$4 x^{2} + 13 x + 10$

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 $a \cdot c = 4 \cdot 10 = 40$ and whose sum is $b = 13$ .

Factor $13$ out of $13 x$ .

$4 x^{2} + 13 (x) + 10$

Rewrite $13$ as $5$ plus $8$

$4 x^{2} + (5 + 8) x + 10$

Apply the distributive property.

$4 x^{2} + 5 x + 8 x + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 5 x) + 8 x + 10$

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

$x (4 x + 5) + 2 (4 x + 5)$

Step 3

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

$(4 x + 5) (x + 2)$

Factor 4x^2+13x+10

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