# How do you factor 7x^2 – 35x + 28?

Jul 27, 2018

$7 {x}^{2} - 35 x + 28 = 7 \left(x - 4\right) \left(x - 1\right)$

#### Explanation:

First, take out the common factor which is $7$

$7 {x}^{2} - 35 x + 28$

$= 7 \left({x}^{2} - 5 x + 4\right)$

$x = \frac{5 \pm \sqrt{25 - 4 \left(1\right) \left(4\right)}}{2 \left(1\right)}$

$x = \frac{5 \pm \sqrt{9}}{2}$

$x = \frac{5 \pm 3}{2}$

$x = \frac{5 - 3}{2}$ or $x = \frac{5 + 3}{2}$

$x = 1$ or $x = 4$

$= 7 \left({x}^{2} - 5 x + 4\right)$

$= 7 \left(x - 4\right) \left(x - 1\right)$

Jul 27, 2018

$7 \left(x - 1\right) \left(x - 4\right)$

#### Explanation:

$\text{take out a "color(blue)"common factor } 7$

$= 7 \left({x}^{2} - 5 x + 4\right)$

$\text{the factors of "+4" which sum to } - 5$

$\text{are "-1" and } - 4$

$= 7 \left(x - 1\right) \left(x - 4\right)$

Jul 28, 2018

$7 \left(x - 1\right) \left(x - 4\right)$

#### Explanation:

Since all terms are divisible by $7$, we can factor this out to get

$7 \left({x}^{2} - 5 x + 4\right)$

What we have in parenthesis can be factored with a little thought experiment:

What two numbers sum up to $- 5$ and have a product of $4$?

After some trial and error, we arrive at $- 1$ and $- 4$. This means we can factor this as

$7 \left(x - 1\right) \left(x - 4\right)$

Hope this helps!