1. ## Remainder Theorem

Hi, Im having troubles in understanding how to solve these two equations and how to divide them.

a) (2x^3 + 5x^2 - 2x - 3) / (x +1)

b) (2x^3 - 7x^2 + 16x - 22) / (2x - 3)

2. Hello,

What do you mean by "solve these equations" ? With an equation comes a = sign, which is not here

You can read this, this or this about polynomial long division (though the latter one is a more complicated example)

3. Originally Posted by flwer_13
Hi, Im having troubles in understanding how to solve these two equations and how to divide them.

a) (2x^3 + 5x^2 - 2x - 3) / (x +1)
x alone divides into 2x^3 2x^2 times. Multiplying x+1 by 2x^2 gives 2x^3+ 2x^2:
(2x^3+ 5x^2- 2x- 3)- (2x^3+ 2x^2)= 3x^2- 2x- 3.

x alone divides into 3x^2 3x times. Multiplying x+1 by 3x gives 3x^2+ 3x:
(3x^2- 2x- 3)- (3x^2+ 3x)= -5x- 3.

x alone divides into -5x -5 times. Multiplying x+1 by -5 gives -5x- 5:
(-5x-3)- (-5x-5)= 2.

(2x^3 + 5x^2 - 2x - 3) / (x +1)= 2x^2+ 3x- 5 with remainder 2.

b) (2x^3 - 7x^2 + 16x - 22) / (2x - 3)
2x divides into 2x^3 x^2 times. Multiplying 2x-3 by x^2 gives 2x^3- 3x^3:
(2x^3- 7x^2+ 16x- 22)- (2x^3- 3x^2)= -4x^2+ 16x- 22.

Can you finish that one?