Quadratic Expressions. Please tell me how to answer these questions fully. State whether there is common factor or pattern. Then use decomposition. D. 6a^2-7a+1   

Expert Answers
lfryerda eNotes educator| Certified Educator

If you have more than one question, you need to make separate posts.

To factor using decomposition, you need to find the factors of the product of the first and last coefficient that add to the middle coefficient.

In this case, we are looking for factors of 6x1=6 that add to -7, which are -6 and -1.

Then split apart the middle term using these factors.  Finally, factor using group factoring twice.

`6a^2-7a+1`   split middle term

`=6a^2-6a-a+1`   factor by grouping

`=6a(a-1)-1(a-1)`   common factoring


The expression factors into `(a-1)(6a-1)` .