How do you factor $3 x^{2} + 4 x + 1$ $3x^2+4x+1$ ??

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How do you factor $3 x^{2} + 4 x + 1$ $3x^2+4x+1$ ??

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Answer 1 · 2015-12-09T01:19:19

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

Explanation:

$3 x^{2} + 4 x + 1$ $3x^2+4x+1$ is a quadratic equation in the form $a x^{2} + b x + c$ $ax^2+bx+c$ , where $a = 3, b = 4, and c = 1$ $a=3, b=4, and c=1$ .

Use the AC method to factor the equation.

Multiply $a$ $a$ times $c$ $c$ .

$3 \times 1 = 3$ $3xx1=3$

Find two numbers that when added equal $4$ $4$ and when multiplied equal $3$ $3$ . The numbers are $3$ $3$ and $1$ $1$ .

Rewrite the equation, substituting the middle term (b) with $3 x$ $3x$ and $x$ $x$ .

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

Group the terms into two groups.

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

Factor $3 x$ $3x$ out of the first group.

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

Factor out $(x + 1)$ $(x+1)$

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

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How do you factor $3 x^{2} + 4 x + 1$ $3x^2+4x+1$ ??

1 Answer

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