Factor. Use factoring by grouping even though it would seem reasonable to first combine like terms

3u^2-7-21u+49

Would be the same procedure as factoring polynomial?
Thanks!

since you have 3u^2, look for multiples of 3:

3u^2-21u = 3u(u-7)

Work on that idea. But why both the -7 and +49 constant terms?

Looks like a typo to me.

That's the actual problem on my assignment.

I am so confused!

Well, there must be a typo somewhere, because if we say -7+49 = 42, then we have

3u^2-21u+42

and that does not factor.

You are probably right but is what the question in the textbook is.

I am unsure of what the answer is.

I'll admit that if the question is unclear, so will be the answer.

Better check with your teacher.

OK I will gt in touch with the teacher.

Thanks!

Yes, factoring by grouping is a common method used to factor polynomials. It is a helpful technique when you have a polynomial with four or more terms.

To factor the given expression, 3u^2 - 7 - 21u + 49, we will use factoring by grouping. Here's how to do it:

Step 1: Group the terms in pairs.
(3u^2 - 7) - (21u - 49)

Step 2: Factor out the greatest common factor from each group.
The first group has a common factor of 1, and the second group has a common factor of -7.
1(3u^2 - 7) - 7(3u - 7)

Step 3: Now, check if you can factor out a common binomial factor from the two grouped terms.
In this case, we notice that (3u - 7) is the common factor.

Therefore, we can factor out (3u - 7) from both terms:
(3u - 7)(u + 1) - 7(3u - 7)

Step 4: Check that both expressions inside the parentheses are the same.
Since both expressions are (3u - 7), we can now factor out the common binomial factor:
(3u - 7)(u + 1 - 7)

Simplifying the resulting expression, we have:
(3u - 7)(u - 6)

So, the factored form of the polynomial 3u^2 - 7 - 21u + 49 is (3u - 7)(u - 6).