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

1 Answer
Jun 15, 2018

(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.