Question

How do you factor the trinomial `5-6x+x^2`?

Answer 1

`(x-5)(x-1)`

Explanation:

As per the question, we have

`5-6x+x^2`

By arranging the terms, we get

`x^2-6x+5`

Now, here we have an equation of the form `ax^2+bx+c` and to further factorise this equation we have to split the middle term `bx` in such a way that it is able to get summed up by the factors of `c`.

As `c = 5`

`:.` Factors of `c` : `1 and 5`

Now, `bx = -6x`

So, we can write `-6x` as `-1x-5x`.

Note : `(-1)xx(-5) = 5 = c`

So, we have the equation as,

`x^2-x-5x+5`

Rearranging the terms,

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

Taking the common terms out,

`x(x-1)-5(x-1)`

Simplifying it further,

`(x-5)(x-1)`

Hence, the answer.