Question

What are the factors of x2 – 100?

A. (x – 50)(x + 50)
B. (x – 10)(x + 10)
C. (x – 25)(x + 4)
D. (x – 5)(x + 20)

Answer 1

• Option B is the correct answer.

Explanation :-

$= > \large \rm {x}^{2} - 100 \\ \\ = \bf {(x)}^{2} - {(10)}^{2} \\ = \bf \red{(x + 10)(x - 10)}$

Answer 2

B.) (x – 10)(x + 10).

• The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element.
• There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
• The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are  called factors. A factor is therefore another number's divisor.

Here, the expression is given as,

$x^{2} -100.$

Now, we know the algebraic identity that is, $a^{2} -b^{2} =(a+b)(a-b).$

Then, we get,

$x^{2} -100\\=x^{2} -10^{2} \\=(x+10)(x-10).$

Hence, option B is correct.

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