Factor 40x^2+97x+45

$40 x^{2} + 97 x + 45$

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 $a \cdot c = 40 \cdot 45 = 1800$ and whose sum is $b = 97$ .

Factor $97$ out of $97 x$ .

$40 x^{2} + 97 (x) + 45$

Rewrite $97$ as $25$ plus $72$

$40 x^{2} + (25 + 72) x + 45$

Apply the distributive property.

$40 x^{2} + 25 x + 72 x + 45$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(40 x^{2} + 25 x) + 72 x + 45$

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

$5 x (8 x + 5) + 9 (8 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $8 x + 5$ .

$(8 x + 5) (5 x + 9)$

Factor 40x^2+97x+45

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