Factor.
15x^4 - 18x^3 + 21x^2 - 9x
The method that I usually use did not seem to work... so I'm not sure if I messed up or not. Please help if you can and explain how you did it!
Thank you! :-)
The only thing that can be factored out is 3x because that's what all of the terms have in common - they're multiples of 3x. So the answer is:
3x(5x^3 - 6x^2 + 7x - 3)
To factor the given expression 15x^4 - 18x^3 + 21x^2 - 9x, we can use the method of factoring by grouping.
Step 1: Group the terms.
Split the given expression into two groups by grouping the first two terms and the last two terms:
(15x^4 - 18x^3) + (21x^2 - 9x)
Step 2: Factor out the common factors from each group.
From the first group, factor out the greatest common factor, which is 3x^3:
3x^3(5x - 6)
From the second group, factor out the greatest common factor, which is 3x:
3x(7x - 3)
Step 3: Factor out the common factor from the entire expression.
Now, we have a common factor of (5x - 6) for the first group and (7x - 3) for the second group, so we can factor those out:
3x^3(5x - 6) + 3x(7x - 3)
Step 4: Combine the factored expressions.
The factored expression is:
3x(5x - 6)(x^2 + 7)
To check your factoring, you can expand the factored expression using the distributive property, and it should simplify back to the original expression.