SOLUTION: I need help really bad..What is a Remainder Theorem? Ihave been working on these problems for over two hours help 1. Use the Remainder Theorem to find the reaminder when f(x) i

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Question 175312: I need help really bad..What is a Remainder Theorem?
Ihave been working on these problems for over two hours help
1. Use the Remainder Theorem to find the reaminder when f(x) is divided by g(x)
1. f(x)=x^4+8x^3+12x^2;g(x)=x+1
2. f(x)=5x^6-3x^3+8;g(x)=x+1
Someone please help m,e on these.....It is important....Thank you
Answer by nycsub_teacher(90) (Show Source):
You can put this solution on YOUR website!
f(x)= x^4+8x^3+12x^2; g(x) = x + 1
I will do the above question and you can do the next one.
Do you see x + 1 as the value for the function g?
You will notice that the quantity has a +1, right?
Let x = the opposite of +1, which is -1.
Everywhere there is an x, replace it with -1 and simplify the polynomial function f.
So, x = -1
f(-1) = (-1)^4 + 8(-1)^3 + 12(-1)^2
f(-1) = 1 - 8 + 12
f(-1) = -7 + 12
f(-1) = 5
The remainder is 5.
This is the basic idea behind the Remainder Theorem.
Do the same with the other polynomial function.
Understood?