Factor 2x^2+15x+25

$2 x^{2} + 15 x + 25$

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 $a \cdot c = 2 \cdot 25 = 50$ and whose sum is $b = 15$ .

Factor $15$ out of $15 x$ .

$2 x^{2} + 15 (x) + 25$

Rewrite $15$ as $5$ plus $10$

$2 x^{2} + (5 + 10) x + 25$

Apply the distributive property.

$2 x^{2} + 5 x + 10 x + 25$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 5 x) + 10 x + 25$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

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

Factor 2x^2+15x+25

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