Question

Use the Factor Theorem to determine whether x-2 is a factor of P(x) = -x^4 + x^3 - x + 7.

Specifically, evaluate P at the proper value, and then determine whether x-2 is a factor.

P(?) =?
is x-2 a factor of P(x)
Is x-2 not a factor pf P(x)

Answer 1

P(2) = -3, x - 2 is not a factor

Explanation:

P(2) = -2^4 + 2^3 - 2 + 7 = -16 + 8 - 2 + 7 = -3 ≠ 0

so x - 2 is not a factor of P(x).

Answer 2

As there is remainder of -3, x -2 is not a factor of P(x)

To check if a function is a factor or not,

• put the given x value

`\sf given \ function: P(x) = -x^4 + x^3 - x + 7`

`\sf given \ x \ value: x - 2 = 0 \rightarrow x = 2`

using the instruction:

`\sf P(x) = -x^4 + x^3 - x + 7`

`\sf P(2) = -(2)^4 + (2)^3 - (2) + 7`

`\sf P(2) = -(16)+8-2+7`

`\sf P(2) = -16 +8 -2+7`

`\sf P(2) = -3`

**
`\sf remainder \ found = -3` **

Therefore, x - 2 is not a factor of
`-x^4 + x^3 - x + 7`