Question

In the polynomial below, what number should replace the question mark toproduce a difference of squares?x + ?x - 25A. 5B. 10C. OΟ ΟD. 25

Answer 1

Question:

In the polynomial below, what number should replace the question mark to produce a difference of squares?

`x^2-?x+25^{}`

Solution:

Take the square root of the first and last terms of the polynomial:

The square root of x^2 is x

The square root of 25 is 5

Then, the given polynomial can be written as:

`x^2-?x+25=(x-5)^2\text{ }`

Now, expand the expression on the right side of the above equation:

`x^2-?x+25=(x-5)^2=x^2-10x+25`

thus, we can conclude that the ? = 10. Then, the correct answer is 10.