How do you factor the trinomial $5x^2+ 6x + 1$ ?

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Answer 1 · 2015-11-27T03:24:56

$5x^2+6x+1=(5x+1)(x+1)$

$5x^2+6x+1$ is a quadratic equation, $ax^2+bx+c$ , where $a=5, b=6, and c=1$ .

Use the AC method.

Multiply $a$ times $c$ .

$5xx1=5$

Determine which numbers when added equal $6$ and when multiplied equal $5$ . The numbers $1$ and $5$ meet the criteria.

Rewrite the trinomial with $5x$ and $x$ in place of $6x$ .

$5x^2+5x+x+1$

Group the first two terms and the last two terms.

$(5x^2+5x)+(x+1)$

Factor out $5x$ from the first group.

$5x(x+1)+1(x+1)$ (I included the $1$ in front of the parentheses so you can see where the final answer comes from.)

Factor out $(x+1)$ .

$(5x+1)(x+1)$

How do you factor the trinomial 5x^2+ 6x + 15x^2+ 6x + 1?