Question:
In the polynomial below, what number should replace the question mark to produce a difference of squares?
[tex]x^2-?x+25^{}[/tex]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:
[tex]x^2-?x+25=(x-5)^2\text{ }[/tex]Now, expand the expression on the right side of the above equation:
[tex]x^2-?x+25=(x-5)^2=x^2-10x+25[/tex]thus, we can conclude that the ? = 10. Then, the correct answer is 10.
