Question

is \\((x + 2)\\) a factor of \\(-4x^4 - 3x^3 + 11x^2 - x + 3\\)?

no, it is a not factor.
yes, it is a factor.

Explanation:

Step1: Identify the polynomial and the divisor

$$P(x) = -4x^4 - 3x^3 + 11x^2 - x + 3$$

$$x - c = x + 2 \implies c = -2$$

Step2: Apply the Factor Theorem

$$P(-2) = -4(-2)^4 - 3(-2)^3 + 11(-2)^2 - (-2) + 3$$

Step3: Evaluate the expression

$$P(-2) = -4(16) - 3(-8) + 11(4) + 2 + 3$$

$$P(-2) = -64 + 24 + 44 + 2 + 3 = 9$$

Step4: Determine if it is a factor

$$P(-2) eq 0 \implies (x+2) \text{ is not a factor}$$

Answer:

No, it is a not factor.