Factor the following binomial.

Question

100x^2 - 1

Select the correct choice below.

(a) 100x^2 - 1=?

(b) The polynomial is prime.

Answer 1

Hi Jamal,

Any time you have want to factor an expression in the form (a - b), you can always break it into

(sqrt(a) + sqrt(b)) (sqrt(a) - sqrt(b))

In this case, "a" would be 100x^2 and "b" would be 1.  

So it can be factored to (10x + 1) (10x - 1)

Answer 2

a) Easiest way to solve this problem is to remember that a² - b² = (a+b) (a-b) and recognize the pattern from the problem

100x²-1 = (10x)² - (1)² = (10x+1)(10x-1)

b) If you do not remember the formula for a² - b², then you will need to solve the problem by using usual factoring method for ax² + bx + c = 100x² + 0x -1 

where a = 100, b = 0, and c = -1.

If factors are m and n

mn = ac = -100 = -1x2x2x5x5

m+n = b = 0

This gives m=10 and n = -10

100x² - 1 = 100x² +10x - 10x - 1 = 10x (10x +1) - 1 (10x +1) = (10x+1)(10x-1)