Question

Use the Factor Theorem to determine whether x-1 is a factor of P(x) = 2x– 3x² - 4x +5.Specifically, evaluate P at the proper value, and then determine whether x - 1 is a factor.P(I) = 0o *- 1 is a factor of P(x)O *- 1 is not a factor of P(x)

Answer 1

Given the function:

`P(x)=2x^3-3x^2-4x+5`

We need to show that, if ( x - 1 ) is a factor of P(x) or not.

So, we need to factor the given function P(x) or substitute with x = 1

If P(x = 1 ) = 0, so, (x - 1 ) will be a factor for P(x)

So, we will substitute with x = 1

`\begin{gathered} P(1)=2\cdot1^3-3\cdot1^2-4\cdot1+5 \\ P(1)=2-3-4+5=7-7=0 \end{gathered}`

As shown, P(1) = 0

So, The factor (x - 1) is a factor of P(x)

So, the answer will be:

P(1) = 0

(x - 1 ) is a factor of P(x)