Question

is \\( (x + 5) \\) a factor of \\( 3x^3 - 70x + 23 \\)?

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

Explanation:

Step1: Identify the polynomial and the divisor

$$P(x) = 3x^3 - 70x + 23, \quad x - c = x + 5 \implies c = -5$$

Step2: Apply the Factor Theorem

$$P(-5) = 3(-5)^3 - 70(-5) + 23$$

Step3: Evaluate the expression

$$P(-5) = 3(-125) + 350 + 23 = -375 + 373 = -2$$

Step4: Determine if it is a factor

$$P(-5) eq 0 \implies (x + 5) \text{ is not a factor}$$

Answer:

No, it is a not factor.