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)