Question

Find the factorization of the polynomial below. 100x^2-20x+1

A. (10x+1)^2
B. (10-1)^2
C. (50x+1)^2
D. (50x-1)^2

Answer 1

Answer:B

Explanation:

Answer 2

The factorization of
`100x^2-20x+1`

is
`(10x-1)^2`.

EXPLANATION

We want to factor
`100x^2-20x+1`

Comparing this to
`ax^2+bx+c`

`a=100,b=-20,c=1`

`ac=100`

We look for factors of 100 that add up to
`-20`.

These factors are
`-10,-10`

We now split the middle term to obtain;

`100x^2-10x-10x+1`

We factor to obtain;

`10x(10x-1)-1(10x-1)`

This simplifies to
`(10x-1)(10x-1)=(10x-1)^2`