Question

How do you factor `x² - 8x + 7`?

Answer 1

`color(green)((x-1)(x-7 )` is the factorised form.

Explanation:

`x^2 - 8x +7`

We can Split the Middle Term of this expression to factorise it.

In this technique, since we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 1*7 =7`
AND
`N_1 +N_2 = b = -8`

After trying out a few numbers we get `N_1 = -1` and `N_2 =-7`
`(-1)*(-7) = 7`, and `-1+(-7)= -8`

`x^2 - 8x +7 = x^2 color(green)(-1x - 7x) +7`

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

`(x-1)` is a common factor to each of the terms

`color(green)((x-1)(x-7 )` is the factorised form.

Answer 2

Factor `y = x^2 - 8x + 7`

Explanation:

Because ( a + b + c = 0), use the shortcut:
One real root is 1, and the factor is (x - 1)
The other real root is `c/a = 7`, then, the corresponding factor is
(x - 7).
Factorised form:
y = (x - 1)(x - 7)