Factor 4r^2+21r+5

$4 r^{2} + 21 r + 5$

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 $b = 21$ .

Factor $21$ out of $21 r$ .

$4 r^{2} + 21 (r) + 5$

Rewrite $21$ as $1$ plus $20$

$4 r^{2} + (1 + 20) r + 5$

Apply the distributive property.

$4 r^{2} + 1 r + 20 r + 5$

Multiply $r$ by $1$ .

$4 r^{2} + r + 20 r + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 r^{2} + r) + 20 r + 5$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 r + 1$ .

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

Factor 4r^2+21r+5

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