Question

If x-1 is a factor of P(x) = x – 5x2 + 7x - 3, which of the followingrepresents the complete factorization for P(x)?A. (1 - 3)(x-1)(+1)O B. (x - 3)(x - 1)(x - 1)c. (x - 1)(+3)(x+1)D. (x-3)(x+3)(x - 1)

Answer 1

Given data:

`P(x)=x^3-5x^2+7x-3`

If (x-1) is a facotr of the given function then we will get,

`(x^3-5x^2+7x-3)/(x-1)=x^2-4x+3`
`x^3-5x^2+7x-3=(x^2-4x+3)(x-1)`

Now, factorizing the quadratic equation,

`\begin{gathered} x^2-4x+3=x^2-3x-x+3 \\ =x(x-3)-1(x-3) \\ =(x-3)(x-1) \end{gathered}`

Thus, the complete fatorization for P(x) is

`x^3-5x^2+7x-3=(x-3)(x-1)(x-1)`

Answer : Option (B)