Question

Check 2 x-1 is a factor of p[x]=x^3-x^2+2x-1

Answer 1

Explanation:

2x - 1 =0

2x = 1

x = 1/2

Now We have to find P(1/2). If P(1/2) is zero, then 2x - 1 is a factor of P(x)

P(x)= x³ - x² + 2x -1

`P((1)/(2))=[(1)/(2)]^(3)-[(1)/(2)]^(2)+2*[(1)/(2)]-1\\\\=(1)/(8)-(1)/(4)+1-1\\\\=(1)/(8)-(1*2)/(4*2)+0\\\\=(1)/(8)-(2)/(8)\\\\=(1-2)/(8)\\\\=(-1)/(8)\\eq 0`

2x - 1 is not a factor of p(x)