Question

Factor the polynomial by GROUPING. Please don’t answer if you aren’t going to show at least a little bit of work.

3r-r^2 + 2r-6

Answer 1

(r - 3)(-r + 2)

Explanation:

• First, we can rearrange the terms of the polynomial to group the first two terms and the last two terms together, which gives us:

(3r - r^2) + (2r - 6)

• Next, we can factor out a common factor from each group.
• We can factor out an r from the first group and a 2 from the second group, which gives us:

r(3 - r) + 2(r - 3)

• Notice that the expressions inside the parentheses are not the same.
• We can make the expressions in the parentheses by using two simple steps.
• First, we can factor out a -1 from (3r - r^2) instead of an r, which gives us:

-1(-3r + r^2) + 2(r - 3)

• Now, we can factor out an r from the first group, which gives us:

-r(-3 + r) + 2(r - 3)

-r (r - 3) + 2(r - 3)

• Now, the expressions inside the parentheses are the same.

We can factor out a common factor of (r - 3)` from both groups to get:

(r - 3)(-r + 2)

So, the polynomial 3r - r^2 + 2r - 6 factors into (r - 3)(-r + 2) when factored by grouping.

I hope this helps! Let me know if you have any further questions.