Question

The polynomial f(x) given below has 1 as a zero.

f(x)=x3−3x2+4x−2?

Answer 1

f(x)=x3−3x2+4x−2

To find if 1 is a zero of the given polynomial, we need to substitute x = 1

f(1) = 1³ - 3(1)² + 4(1) -2

f(1) = 1 - 3 +4 -2

f(1) = 5 - 5 = 0

Since f(1) comes to 0 hence x = 1 is the zero of the polynomial.

Sine x = 1 is the root of the function (x-1) will divide the polynomial f(x)

Hence f(x) = (x-1)(x^2-2x+2)