19. Which is NOT a zero of the following function? $$ f(x)=x^{3}+3 x^{2}-x-3 $$ A. 1 B. -1 C. 3 D. -3

Question

UpStudy AI · Accepted Answer

We are given the function

$$
f(x)=x^{3}+3 x^{2}-x-3
$$

and we need to find which of the following options is **not** a zero of $$ f(x) $$:  
A. $$ 1 $$  
B. $$ -1 $$  
C. $$ 3 $$  
D. $$ -3 $$

**Step 1: Test $$ x = 1 $$**

Substitute $$ x = 1 $$ into the function:

$$
f(1)=1^{3}+3(1)^{2}-1-3 = 1+3-1-3 = 0
$$

Since $$ f(1)=0 $$, $$ 1 $$ is a zero of $$ f(x) $$.

**Step 2: Test $$ x = -1 $$**

Substitute $$ x = -1 $$ into the function:

$$
f(-1)=(-1)^{3}+3(-1)^{2}-(-1)-3 = -1+3+1-3 = 0
$$

Since $$ f(-1)=0 $$, $$ -1 $$ is a zero of $$ f(x) $$.

**Step 3: Test $$ x = 3 $$**

Substitute $$ x = 3 $$ into the function:

$$
f(3)=3^{3}+3(3)^{2}-3-3 = 27+27-3-3 = 48
$$

Since $$ f(3)=48 \neq 0 $$, $$ 3 $$ is **not** a zero of $$ f(x) $$.

**Step 4: Test $$ x = -3 $$**

Substitute $$ x = -3 $$ into the function:

$$
f(-3)=(-3)^{3}+3(-3)^{2}-(-3)-3 = -27+27+3-3 = 0
$$

Since $$ f(-3)=0 $$, $$ -3 $$ is a zero of $$ f(x) $$.

**Conclusion:**  
The only option that is not a zero of the function is $$ 3 $$.
The answer is C. 3

19. Which is NOT a zero of the following function? \[ f(x)=x^{3}+3 x^{2}-x-3 \] A. 1 B. -1 C. 3 D. -3