Question

Find the remainder when the $4{x^3} - 3{x^2} + 4x - 2$ is divided by
${\text{A}}{\text{.}}$ x-1
${\text{B}}{\text{.}}$ x-2

Answer 1

Hint: Make the divisor equal to 0 and then substitute the value of x in the dividend. Doing this we will get a value of the dividend which will be our remainder.

Complete step-by-step answer:

We have x-1
x-1=0
x=1
Put this in the dividend:
$4{(1)^3} - 3{(1)^2} + 4(1) - 2 = 3$
So, the remainder is 3.

Now we have x-2
x-2=0
x=2
Put this in the dividend:
$4{(2)^3} - 3{(2)^2} + 4(2) - 2 = 26$
So the remainder is 26.

NOTE: As p(x) = q(x).g(x) + r(x)
Where, p(x)= dividend, q(x)=quotient, g(x)=divisor and r(x)=remainder
To get the values of x we equate g(x) with 0. Now, if we substitute the value of x at LHS and RHS then, g(x) becomes 0, so g(x).q(x)=0 So, then we are left with, p(x)=r(x). Long division method could also be used to get the remainder.