Factor each polynomial by grouping. Check your answer.
1. 2r^2 - 6r + 12 - 4r
2r(r-3) - 4(r-3)
...
To factor the polynomial by grouping, we will first group the terms in pairs. Let's rearrange the terms:
2r^2 - 6r - 4r + 12
Now let's factor out the greatest common factor (GCF) from the first two terms and the last two terms separately:
2r(r - 3) - 4(r - 3)
Notice that the term (r - 3) is common in both groups. We can factor it out:
(r - 3)(2r - 4)
Now let's check if our factored expression is correct by expanding it:
(r - 3)(2r - 4) = 2r(r) - 2r(3) - 4(r) + 4(3)
= 2r^2 - 6r - 4r + 12
Our factored expression matches the original polynomial, so our answer is correct.