Factor 3x^2+4x+1

$3 x^{2} + 4 x + 1$

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 $a \cdot c = 3 \cdot 1 = 3$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

$3 x^{2} + 4 (x) + 1$

Rewrite $4$ as $1$ plus $3$

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 3x^2+4x+1

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