Factor 4r^2+9r+5

$4 r^{2} + 9 r + 5$

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 $a \cdot c = 4 \cdot 5 = 20$ and whose sum is $b = 9$ .

Factor $9$ out of $9 r$ .

$4 r^{2} + 9 (r) + 5$

Rewrite $9$ as $4$ plus $5$

$4 r^{2} + (4 + 5) r + 5$

Apply the distributive property.

$4 r^{2} + 4 r + 5 r + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 r^{2} + 4 r) + 5 r + 5$

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

$4 r (r + 1) + 5 (r + 1)$

Step 3

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

$(r + 1) (4 r + 5)$

Factor 4r^2+9r+5

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