# How do you factor the expression 3x^2+ 10x + 7?

$\left(x + 1\right) \left(3 x + 7\right)$

#### Explanation:

$3 {x}^{2} + 10 x + 7$

$= 3 {x}^{2} + 3 x + 7 x + 7$

$= 3 x \left(x + 1\right) + 7 \left(x + 1\right)$

$= \left(x + 1\right) \left(3 x + 7\right)$

Jul 27, 2018

$p \left(x\right) = \left(x + 1\right) \left(3 x + 7\right)$

#### Explanation:

Let ,

$p \left(x\right) = 3 {x}^{2} + \textcolor{red}{10 x} + 7$

Here ,

color(blue)(3 xx7=21 and 3+7=10

$\therefore p \left(x\right) = \underline{3 {x}^{2} + \textcolor{red}{3 x}} + \underline{\textcolor{red}{7 x} + 7}$

$\therefore p \left(x\right) = 3 x \left(x + 1\right) + 7 \left(x + 1\right)$

$\therefore p \left(x\right) = \left(x + 1\right) \left(3 x + 7\right)$

Jul 28, 2018

$\left(3 x + 7\right) \left(x + 1\right)$

#### Explanation:

We can use the strategy factoring by grouping. Here, we can split up the $b$ term so we can factor the left and right sides.

Here's what I mean. We can rewrite this as

$\textcolor{s t e e l b l u e}{3 {x}^{2} + 3 x} + \textcolor{p u r p \le}{7 x + 7}$

Out of the blue term, we can factor out a $3 x$, and the purple term, we can factor out a $7$. This leaves us with:

$\textcolor{s t e e l b l u e}{3 x \left(x + 1\right)} + \textcolor{p u r p \le}{7 \left(x + 1\right)}$

Since both terms have an $x + 1$ in common, we can factor that out to get

$\left(3 x + 7\right) \left(x + 1\right)$

Hope this helps!