Factor 7x^2+22x+3

$7 x^{2} + 22 x + 3$

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 $a \cdot c = 7 \cdot 3 = 21$ and whose sum is $b = 22$ .

Factor $22$ out of $22 x$ .

$7 x^{2} + 22 (x) + 3$

Rewrite $22$ as $1$ plus $21$

$7 x^{2} + (1 + 21) x + 3$

Apply the distributive property.

$7 x^{2} + 1 x + 21 x + 3$

Multiply $x$ by $1$ .

$7 x^{2} + x + 21 x + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + x) + 21 x + 3$

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

$x (7 x + 1) + 3 (7 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 1$ .

$(7 x + 1) (x + 3)$

Factor 7x^2+22x+3

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