SOLUTION: 1.) Explain the difference between using the remainder theorem and synthetic division in finding the remainder when P(x) is divided by x-r.

Question 985333: 1.) Explain the difference between using the remainder theorem and synthetic division in finding the remainder when P(x) is divided by x-r.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

I think you're asking what is the difference between the 
remainder theorem and the factor theorem?

The Remainder Theorem:

When we divide a polynomial f(x) by x-c the remainder equals f(c)

The Factor Theorem:

When f(c)=0 then x-c is a factor of the polynomial
When x-c is a factor of the polynomial then f(c)=0

-----------------------------

1.  Use the remainder theorem to find what you get when you substitute
    -3 for x in f(x) = 3x^3 - 5x^2 + 7x - 4, whch is f(-3).  Then check 
    your answer by actually substituting -3 in f(x) to find f(-3)

    -3 | 3   -5    7    -4
       |     -9   42  -147
         3  -14   49  -151

So f(-3) = -151, the number in the lower right corner of the synthetic division. 

Checking by actually substituting -3 for x in f(x)

f(x) = 3x^3 - 5x^2 + 7x - 4
f(-3) = 3(-3)^3 - 5(-3)^2 + 7(-3) - 4
f(-3) = 3(-27) - 5(9) -21 - 4
f(-3) = -81 - 45 - 21 - 4
f(-3) = -151


2.  Use the factor theorem to show that x-2 is a factor of x^4-7x^2+x+10

2 | 1  0 -7  1  10
  |    2  4 -6 -10 
    1  2 -3 -5   0

Edwin

RELATED QUESTIONS
1.) Explain the difference between using the remainder theorem and synthetic division in... (answered by Alan3354)

Explain the difference between using the remainder theorem and synthetic division in... (answered by MathLover1)

Explain the difference between using the remainder theorem and synthetic division in... (answered by Alan3354)

Explain the difference between using the remainder theorem and synthetic division when... (answered by Edwin McCravy)

Explain the difference between using the remainder theorem and synthetic division when... (answered by ikleyn)

p(x)=x^3-x+1 c=1/2 solve by using synthetic division and the remainder... (answered by stanbon)

p(x)=8x^2+6x+2, c=1/2 Use synthetic division and the remainder theorem to find p(c)... (answered by Edwin McCravy)