If f(x)=x^4-4x^3+3x^2-2x+1, then find whether f(0)xf(-1)=f(2).​

It is given that f(0)=1 and f(1)=4 for the polynomial f(x)=4x

3

−3x

2

+2x+k, therefore, we substitute the values and find the value of k as shown below:

Whenf(0)=1

f(0)=4(0)

3

−3(0)

2

+2(0)+k

⇒1=k

Whenf(1)=4

f(1)=4(1)

3

−3(1)

2

+2(1)+k

⇒4=4−3+2+k

⇒4=3+k

⇒k=4−3

⇒k=1

We conclude that, in both the cases k=1, thus, we substitute k=1 in f(x):

f(x)=4x

3

−3x

2

+2x+1

Hence, f(x)=4x

3

−3x

2

+2x+1.