Question

WILL MARK BRAINLIEST - 75 POINTS!!
Find the factorization for the polynomial 100x^2- 20x+1

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

Answer 1

Answer:

$(10x-1)^2$

Step-by-step explanation:

Here we are going to apply the rule of "Square of the difference". The rule is as given below

$(a-b)^2=a^2-2 \times a \times b + b^2$   ---------(A)

Now we have our original polynomial as

$100x^2-20x+1$

Which can be re written as

$(10x)^2-2 \times 10x \times 1 + 1^2$  ---------------(B)

Hence comparing it with (A)

$a=10x$

$b=1$

Applying the rule on (B)

$(10x)^{2}-2 \times 10x \times 1 + 1^2 = (10x-1)^2$

Hence our answer is

$(10x-1)^2$

Answer 2

Answer:

$\huge \boxed{\bold{C.} \ (10x-1)^2}$

Step-by-step explanation:

$100x^2- 20x+1$

Rewriting -20x as -10x-10x.

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

Factoring the two groups.

$10x(10x-1)-1(10x-1)$

Taking (10x - 1) as a common factor.

$(10x-1)(10x-1)$

$(10x-1)^2$