Factor 3x^2+22x+7

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

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

Factor $22$ out of $22 x$ .

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

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

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 1$ .

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

Factor 3x^2+22x+7

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