Question

How do you factor `7x^2 – 35x + 28`?

Answer 1

`7x^2-35x+28=7(x-4)(x-1)`

Explanation:

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

`7x^2-35x+28`

`=7(x^2-5x+4)`

Using quadratic formula,

`x=(5+-sqrt(25-4(1)(4)))/(2(1))`

`x=(5+-sqrt9)/2`

`x=(5+-3)/2`

`x=(5-3)/2` or `x=(5+3)/2`

`x=1` or `x=4`

`=7(x^2-5x+4)`

`=7(x-4)(x-1)`

Answer 2

`7(x-1)(x-4)`

Explanation:

`"take out a "color(blue)"common factor "7`

`=7(x^2-5x+4)`

`"the factors of "+4" which sum to "-5`

`"are "-1" and "-4`

`=7(x-1)(x-4)`

Answer 3

`7(x-1)(x-4)`

Explanation:

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

`7(x^2-5x+4)`

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(x-1)(x-4)`

Hope this helps!