please help!!?

Question

Determine whether the trinomial below is a difference of squares, a perfect square trinomial, just factorable, or nonfactorable.
x2 - 10x + 25

A. difference of squares
B. perfect square trinomial
C. nonfactorable
D. factorable

Answer 1

B
x^2-10x+25
=(x)^2-2*x*5+(5)^2
=(x-5)^2
Please note that as the expression is a perfect square trinomial,it is also factorable.

Answer 2

To answer this question, the easiest thing to do is to factor it. Then, you can look at the answer and determine what kind of factoring it was, whether perfect square, difference, etc.

To start, look at your constant in the equation, 25. Let's look at all the ways we can factor 25: 25x1, 5x5. We know that these numbers either have to be both positive or both negative, since 25 is positive [a pos times a pos or a neg times a neg. number is positive]

Now let's look at the coefficient on the x , -10. We want to see if a certain combination of the above factors will give us a -10, either by adding them, subtracting them, making them positive/negative, etc. We can see that no combination of 25 and 1 can give us -10: 25 -1, 25+ 1, 1-25, -1 - 25.. .none of these come out to -10.

Now let's move on to 5 & 5. Try: 5 + 5, 5-5, -5-5... we see that a negative 5 minus 5 equals - 10. Perfect, since this is what we need!

So we have: (x -5) (x-5) = x^2 -10x + 25

Now, (x-5) (x-5) can be further simplified to (x-5) ^2.
This is called a perfect square! [B]

And that is your answer. Try using this method each time you have to factor an expression

Answer 3

It's a square: (x-5)².
How can you tell?
If your trinomial is ax² + bx + c
compute b²-4ac. If it is 0, your trinomial is a square.
Here b³-4ac = 100-100 = 0,
so we do indeed have a square.