2x cubed minus x squared minus 6x plus 3. I know the answer is (2x-1)(x squared-3). Please help me with how they got that answer. Thank you!
see other post. It is not necessary to post multiple times.
To factor the expression 2x^3 - x^2 - 6x + 3, we can use a method called factoring by grouping. Here's how you can do it step by step:
Step 1: Group the terms in pairs.
- Group the first two terms (2x^3 - x^2) and the last two terms (-6x + 3).
Step 2: Find the Greatest Common Factor (GCF) of each group.
- In the first group, the GCF is x^2, because x^2 is the highest power of x that can be factored out from both terms.
- In the second group, the GCF is -3, because -3 is the greatest number that can be factored out from both terms.
Step 3: Factor out the GCF from each group.
- From the first group, factor out x^2 to get x^2(2x - 1).
- From the second group, factor out -3 to get -3(2x - 1).
Step 4: Check if the factors from each group are the same.
- In this case, we have (2x - 1) as the common factor from both groups.
Step 5: Combine the common factor from each group.
- We can write the final factored form as (2x - 1)(x^2 - 3).
So, the factored form of the expression 2x^3 - x^2 - 6x + 3 is (2x - 1)(x^2 - 3).