I am down to 5 out of 49 problems that I can't figure out. Help is very much appreciated. Thanks !

Factor by grouping

35x^3 -20 x^2 + 21x -12

5x^2(7x -4) +3(7x -4) = (5x^2 +3)(7x -4)

Thank you very much !

To factor the expression 35x^3 - 20x^2 + 21x - 12 by grouping, we need to group the terms together in a way that allows us to factor out a common factor.

First, let's group the terms:

(35x^3 - 20x^2) + (21x - 12)

Now, we'll factor out the common factors from each group separately.

Taking the first group (35x^3 - 20x^2), we can factor out 5x^2 as the greatest common factor:

5x^2(7x - 4)

Next, we'll take the second group (21x - 12) and factor out the greatest common factor, which is 3:

3(7x - 4)

Now, we have:

5x^2(7x - 4) + 3(7x - 4)

Notice that both groups now have a common factor of (7x - 4). We can now factor out this common factor:

(7x - 4)(5x^2 + 3)

Therefore, the fully factored expression is:

(7x - 4)(5x^2 + 3)