Question

When asked to factor the x^2-100 , a student gives the answer (x-10)(x-10) What is the wrong with this answer?

Answer 1

x^2-100
(x-10)(x+10) ...
a^2-b^2 ---> (a-b)(a+b)

Answer 2

The student took one factor wrong.

Explanation:

We are given that,

The student factored the polynomial as given below,

`x^2-100=(x-10)(x-10)`

i.e.
`x^2-10^2=(x-10)(x-10)`

Since, we know the property,

`a^2-b^2=(a+b)(a-b)`

So, the correct factorization is,

`x^2-10^2=(x+10)(x-10)`

Thus, the student took one factor wrong.