Can someone please explain step by step how to solve this: Factor by Grouping: 8x^3-8x^2-x+1This is for a developmental math class, its the first math I've done in maybe 5-6 years, so I'm very...
Can someone please explain step by step how to solve this:
Factor by Grouping:
This is for a developmental math class, its the first math I've done in maybe 5-6 years, so I'm very rusty, thanks so much.
No problem. As there are 4 terms, we must group to factor. First:
Put () around the first two terms and second two terms.
Next, factor each quantity separately. The biggest thing in common in the first set is 8x^2, leaving you with: 8x^2(x-1) and then you factor out the biggest thing in common in the second quantity, with the goal ALWAYS being to be left with identical terms in both quantities.
What do you have to factor out of the second set of () to be left also with (x-1)? You must factor out a -1, leaving the problem as:
8x^2(x-1)-1(x-1): Understand that facotring out means finding the largest number and variables common to each term.
Now, you have two terms left(terms being groupings separated by + or - signs.) Both terms have a (x-1) in common. Factor that out from both terms and you have your answer:
`8x^3-8x^2-x+1` the first step is to group the number
`(8x^3-8x^2)(-x+1)` looked for the biggest number the number in the parentheses have in common
`8x^2(x-1) -1(x-1) ` now group the numbers on the outside of the parenthesis together
`(x-1) (8x^2-1)` and Voila! You're done.
8x^3-8x^2-x+1 In this expression we group (8x^3-8x^2) together and group (-x+1) together, because in the first group (8x^3-8x^2) when we take the largest term (8x^2 ) common it leaves the factor (x-1) and from the second term when we take (-1) common [ nothing else is common ] it also leaves the same factor (x-1). Hence the process will be like as follow :
=> 8x^2(x-1) - 1(x-1)
=> (x-1)(8x^2 - 1)
Since none of the factors can be factorised further Hence,
the answer is : (x-1)(8x^2-1)(