Can someone explain Remainder Theorem to me?

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Answer 1 · 2018-06-12T21:11:05

#P = DQ + R#

#D(x_0) = 0#

#P(x)# divided by #D(x)# equals #Q(x)# with remainder #R(x)#.

If #x_0# is a root of #D(x)#, then #P(x_0) = R#

Answer 2 · 2018-06-15T13:39:59

Remainder theorem states that;

If a polynomial #f(x)# is divided by #(ax + b),# the remainder #R = f(-b/a)#, which is the value of the polynomial #f(x)#

When;

#x = -b/a#

Examples

Find the positive root of this equation using newton-raphson method to #4# decimal place

#2x³ - 7x² - x + 12#

Note: THIS QUESTION IS FROM APPLICATION OF REMAINDER THEOREM

Now for this;

Find the remainder when #2x³ + 3x - 5# is divided by #(x - 1)#

Simply let #x - 1 = 0#

#x = 1#

Put #x = 1# in #f(x)# and what you get is the remainder..

Find the remainder when #2x³ + 3x² - 1# is divided by #(x² - x - 2)#

Let #x² - x - 2 = 0#

Solve to get the value of #x#, then substitute in #f(x)# to attain the remainder..