Question

(x + 1) is a factor of 3x⁴ - 5x³ + kx - 2. what is the value of k? type your answer in the boxes

Explanation:

Step1: Apply Factor Theorem

If $(x+1)$ is a factor, then $f(-1)=0$ where $f(x)=3x^4 -5x^3 +kx -2$.

Step2: Substitute $x=-1$ into $f(x)$

$$f(-1)=3(-1)^4 -5(-1)^3 +k(-1) -2 = 0$$

Step3: Simplify the equation

$$3(1) -5(-1) -k -2 = 0 \implies 3 +5 -k -2 =0 \implies 6 -k =0$$

Step4: Solve for $k$

$$k=6$$

Wait, correction in calculation: $3 +5 -2 =6$, so $6 -k=0 \implies k=6$. Yes, that's right. Final answer is 6.

Step1: Use Factor Theorem

Set $x=-1$ in polynomial, result=0.

Step2: Substitute $x=-1$

$$3(-1)^4 -5(-1)^3 +k(-1)-2=0$$

Step3: Simplify terms

$$3+5 -k -2=0$$

Step4: Solve for $k$

$$6 -k=0 \implies k=6$$

Answer:

4