Solution:Now considering from the question we have the polynomial 4x3−5x2+6x−2 which is divided by x−1 .
From the basic concept we know that the remainder when a polynomial is divided by another polynomial x−a is given by setting the x−a=0 and then solving for x and substituting the x=a in the polynomial.
So here we need to substitute x=1 as the dividend is x−1 in the divisor 4x3−5x2+6x−2.
After that we will have 4(1)3−5(1)2+6(1)−2 .
After further simplifying we will have 4−5+6−2=10−7=3 .
Hence we can conclude that the remainder when 4x3−5x2+6x−2 is divided by x−1 is 3.