Factor the expression below.[tex]x^{2} - 10x + 25[/tex]A. (x - 5)(x - 5)B. (x + 5)(x + 5) C. (x - 5)(x + 5) D. 5(x2 - x + 5)

Answer:A. (x - 5)(x - 5)Step-by-step explanation:We will do this the old fashioned way...just plain old factoring.  This polynomial is of the form[tex]y=ax^2+bx+c[/tex]The product of a and c have to add up to equal the "middle" term, -10.  a = 1, b = -10, c = 25a * c = 1 * 25 = 25Now we need the factors of 25 to find the combination of factors that will result in a -10.  The factors of 25 are: 1, 25 and 5, 55 and 5 add up to be 10, but since we need a -10, we will use -5 and -5.  The product of -5 * -5 = 25, so we are not messing anything up by using the negative 5.Putting them in order in standard form we have[tex]x^2-5x-5x+25[/tex]Factor by grouping:[tex](x^2-5x)-(5x+25)[/tex]There is an x common to both terms in the first set of parenthesis, so we will factor that out; there is a 5 common to both terms in the second set of parenthesis, so we will factor that out:x(x - 5) - 5(x - 5)NOW what's common in both terms is the (x - 5) so we factor THAT out, and what's left gets grouped together:(x - 5)(x - 5)