Need Help: Polynomials

[jazzdevil]

From my textbook, and I cannot solve it. ?

 

[Dr.Peterson]

In order to help you solve it, we need to know where you are stuck, and what you know that we can make use of.

Do you know the remainder theorem, which would help you write expressions for R₁ and R₂ in terms of a? If so, then you could solve an equation for a.

Or have to tried that already, and just didn't get the right answer? Let us know.

 

[JeffM]

Have you calculated the two remainders indicated?

If so, what did you get?

 

[ksdhart2]

Just in the interest of full disclosure, this exact same problem was also posted on the Askmath subreddit. It was almost certainly posted by the same person, as the usernames are nearly identical - on Reddit they're Jazzydevil.

On that thread, after being so prompted, the OP expanded on what they've already tried:

[I tried]
\(2{(x^3+2x^2-5ax-7)/(x+1)}+(x^3+ax^2-12x+6)/(x-2)=6\)
After this everything got messy...

Additionally, the OP replied to a different user who gave a hint regarding synthetic division, stating "No idea," indicating they are unfamiliar with synthetic division as a concept. However, they were given a very hint that they have yet to reply to:

The factor theorm! the remainder of: f(x)/(x-c) equals f(c). plug in -1 and 2 respectivly in the functions and you will get \(R_1\) and \(R_2\) in terms of a.