Polynomial Long Division Remainder

[michaelcaba]

I am studying to possibly take the CLEP College Algebra Exam. One of the practice questions is to find the remainder of the polynomial long division problem of dividing

by x+1. I cannot find any text or website that explains this type of problem. Can someone show me the steps, or possibly tell me where I can learn the steps? Thank you.

 

[MarkFL]

According to the polynomial remainder theorem, the remainder of the division will be:

[MATH]f(-1)=?[/MATH]

Polynomial remainder theorem - Wikipedia

en.wikipedia.org

 

[michaelcaba]

Thanks! I will track that down.

 

[michaelcaba]

May I ask one more question? If so, why -1?

 

[michaelcaba]

Never mind, I figured out the -1. It comes from (x+1), namely, it is the negation of the 1, correct?

 

[MarkFL]

Never mind, I figured out the -1. It comes from (x+1), namely, it is the negation of the 1, correct?

It comes from the root of:

[MATH]x+1=0\implies x = -1[/MATH]

 

[michaelcaba]

Helpful as always!

 

[michaelcaba]

OK. I totally solved it. Very much appreciated!

 

[HallsofIvy]

You can also think of it as x+ 1= x- (-1). The remainder of polynomial P(x), divided by x- a, is P(a) because if P(x)/(x-a) has Quotient Q(x) with remainder R(x) then P(x)= (x- a)Q(x)+ R(x). So P(a)= (a-a)Q(a)+ R(a)= R(a).