Use the remainder theorem to find the remainder when 2x^3 - 1x^2 + 9x - 25 is divided by x + 4.?

Question

Use the remainder theorem to find the remainder when 2x^3 - 1x^2 + 9x - 25 is divided by x + 4.

Answer 1

Let me see if I remember this correctly:

you get the value of x in x+4 since it is a factor of the equation
x+4=0
x=-4

then substitute the value of x to the equation
P(x)=2x^3 - 1x^2 + 9x - 25
P(-4) = 2(-4)^3 - 1(-4)^2 +9(-4) - 25
P(-4)= -128 - 16 -36 - 25
p(-4) = -205

-205 or -205/x+4 is the remainder(depends on how you're supposed to write it)

Answer 2

Divisor is x + 4

=> x + 4 = 0
=> x = -4

Dividend => 2x^3 - 1x^2 + 9x -25


Remainder Theorem:


2 -1 +9 -25 |_ -4

-8 -28 -148
+ + +
-------------------------------------------------------------------------
2 +7 + 37 123



Therefore:

Remainder = 123

Answer 3

the rest theorem: f(x) = q(x)g(x) + r(x) g(x) is the divisor, q(x) the quotient and r(x) the rest. clearly r(x) is of lesser degree than g(x). contained regarding linear g(x) then r(x) is a few consistent r. What this boils right down to is that if f(x) is split via (x-a) then f(a) = r subsequently you realize that f(2) = 5

Answer 4

6(-4)^-2(-4)^+9(-4)-25=R(x)
-384-8-36-25=R(x)
-453=R(x)

Answer 5

- 4 |2__-1__9__-25
----|___-8__36_-180
----|2__-9__45__-205

R = - 205