Factor 9x^2+46x+5

$9 x^{2} + 46 x + 5$

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 $a \cdot c = 9 \cdot 5 = 45$ and whose sum is $b = 46$ .

Factor $46$ out of $46 x$ .

$9 x^{2} + 46 (x) + 5$

Rewrite $46$ as $1$ plus $45$

$9 x^{2} + (1 + 45) x + 5$

Apply the distributive property.

$9 x^{2} + 1 x + 45 x + 5$

Multiply $x$ by $1$ .

$9 x^{2} + x + 45 x + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 x^{2} + x) + 45 x + 5$

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

$x (9 x + 1) + 5 (9 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $9 x + 1$ .

$(9 x + 1) (x + 5)$

Factor 9x^2+46x+5

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