25x^2 - 60x + 36
highest number they all go into is 1
so would this be Prime?
25 = 5 * 5 or 25*1
36 is 1*36, 2*18, 3*12 , 4*9 , 6*6
hmm, 6 times 5 is 30 and two 30s is 60
so try
(5 x - 6)(5x-6)
ok when I foil that I get the equation
so I would I show my work?
The only thing I can suggest is show all the factors of 25 and 36 as I did.
thanks
To determine whether the given expression, 25x^2 - 60x + 36, is prime, we need to check if it can be factored further. Let's start by factoring out the greatest common factor (GCF) from all the terms.
GCF of 25, -60, and 36 is 1 (since 1 is the highest number they all go into).
By factoring out the GCF of 1, we get:
1(25x^2 - 60x + 36)
Now, let's check if the expression inside the parentheses, 25x^2 - 60x + 36, can be factored.
To do that, we can look for two numbers that multiply to 36 and add up to -60 because these will be the coefficients of the factors when factored.
The numbers that fit these criteria are -6 and -6 (since -6 * -6 = 36 and -6 + -6 = -12 + -48 = -60).
Therefore, we can factor 25x^2 - 60x + 36 as:
1(25x^2 - 6x - 6x + 36)
Now, we can group the terms:
1[(25x^2 - 6x) + (-6x + 36)]
Factor out the greatest common factor from each pair of terms:
1[ x(25x - 6) - 6(25x - 6)]
Now, notice that we have a common binomial factor of (25x - 6) in both terms:
1[(25x - 6)(x - 6)]
So, the fully factored form of 25x^2 - 60x + 36 is:
(25x - 6)(x - 6)
Since the expression can be factored, it is not a prime expression.