# How do you factor by grouping 3x^2 - 17x + 10?

Aug 10, 2018

$3 {x}^{2} - 17 x + 10 = \left(3 x - 2\right) \left(x - 5\right)$

#### Explanation:

In the quadratic polynomial $3 {x}^{2} - 17 x + 10$, the coefficient of ${x}^{2}$ and constant term are of same sign and their product is $30$,

hence we should split $- 17$, the coefficient of $x$. in two parts, whose sum is $17$ and product is $30$. These are $2$ and$15$ and hence

$3 {x}^{2} - 17 x + 10$

= $3 {x}^{2} - 15 x - 2 x + 10$

= $3 x \left(x - 5\right) - 2 \left(x - 5\right)$

= $\left(3 x - 2\right) \left(x - 5\right)$

Note - If sign of coefficient of ${x}^{2}$ and constant term are different, find two numbers whose difference is equal to the coefficient of $x$.

Aug 10, 2018

$\left(x - 5\right) \left(3 x - 2\right)$

#### Explanation:

$\text{factor the quadratic using the a-c method}$

$\text{the factors of the product } 3 \times 10 = 30$

$\text{which sum to "-17" are "-15" and } - 2$

$\text{split the middle term using these factors}$

$3 {x}^{2} - 15 x - 2 x + 10 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{3 x} \left(x - 5\right) \textcolor{red}{- 2} \left(x - 5\right)$

$\text{take out the "color(blue)"common factor } \left(x - 5\right)$

$= \left(x - 5\right) \left(\textcolor{red}{3 x - 2}\right)$

$3 {x}^{2} - 17 x + 10 = \left(x - 5\right) \left(3 x - 2\right)$