15x squared - 35x + 10factor the expression

15x^2-35x+10

5(3x^2-7x+2)
5(3x-1)(x-2)

To factor the expression 15x² - 35x + 10, we can use a method called grouping.

First, look for a common factor among the coefficients of the three terms. In this case, the common factor is 5. So we can rewrite the expression as:

5(3x² - 7x + 2)

Now, we need to find two numbers that multiply to give us the constant term (2), and add up to give us the coefficient of the middle term (-7). In this case, those two numbers are -1 and -2.

Next, we rewrite the middle term (-7x) using these two numbers (-1 and -2):

5(3x² - x - 6x + 2)

Now, we group the terms:

5((3x² - x) + (-6x + 2))

We can now factor out the greatest common factor from each group:

5(x(3x - 1) - 2(3x - 1))

Notice that we now have a common binomial factor of (3x - 1):

5(3x - 1)(x - 2)

Therefore, the factored form of the expression 15x² - 35x + 10 is 5(3x - 1)(x - 2).