Doubt in factoring a trinomial

[mathlearn]

Hey (Wave) (Party),

Problem

Factor $3x^2+11x+10$

Workings

This expression can be separated into,

$3x^2+10x+x+10$

Where have i done wrong ? (Thinking)

Many Thanks :)

 

[MarkFL]

What I would do here is observe that:

\(\displaystyle 3\cdot10=30\)

\(\displaystyle 6\cdot5=30\)

\(\displaystyle 6+5=11\)

Hence:

\(\displaystyle 3x^2+11x+10=(3x+5)(x+2)\)

 

[mathlearn]

What I would do here is observe that:

\(\displaystyle 3\cdot10=30\)

\(\displaystyle 6\cdot5=30\)

\(\displaystyle 6+5=11\)

Hence:

\(\displaystyle 3x^2+11x+10=(3x+5)(x+2)\)

Did you multiply the expression by 3 (Happy) to get 30.

 

[MarkFL]

Did you multiply the expression by 3 (Happy) to get 30.

I multiplied the first coefficient by the last to get 30, and then looked for two factors of this product whose sum is 11, which are 6 and 5.

Here's a tutorial I wrote on the subject:

http://mathhelpboards.com/math-notes-49/factoring-quadratics-3396.html

 

[Greg]

Alternatively,

$$\begin{align*}3x^2+11x+10&=3x^2+5x+6x+10 \\
&=x(3x+5)+2(3x+5) \\
&=(3x+5)(x+2)\end{align*}$$