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

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Answer 1 · 2015-11-21T17:56:34

$6a^2+2a+3a+1=(2a+1)(3a+1)$

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

Use the AC method of factoring.

Multiply $a$ times $c$ .

$6xx1=6$

Determine two numbers that when multiplied equal $6$ and when added equal $5$ . The numbers $2$ and $3$ meet the criteria.

Rewrite the equation with $2a and 3a$ in place of $5a$ .

$6a^2+2a+3a+1$

Group each pair of terms.

$(6a^2+2a)+(3a+1)$

Factor out $2a$ from the first pair of terms.

$2a(3a+1)+1(3a+1)$
I'm showing the $1$ in front of $(3a+1)$ so that it is easier to see where $(2a+1)$ comes from.

Factor out $(3a+1)$ and rewrite.

$(2a+1)(3a+1)$

How do you factor the trinomial 6a^2 +5a+16a^2 +5a+1?