Identify the coefficient of each term in the expression, and give the number of terms. $$ x+4 x^{2}+5 x^{3} $$ Select the correct choice below and fill in the answer box to complete your choice. A. There are three terms. The coefficient of the first term is $$ \square $$, the coefficient of the second term is $$ \square $$, and the coefficient of the third term is B. There are two terms. The coefficient of the first term is $$ \square $$ and the coefficient of the second term is $$ \square $$. There is one term. The coefficient of the term is $$ \square $$. C.

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UpStudy AI · Accepted Answer

To analyze the expression $$ x + 4x^{2} + 5x^{3} $$, we will identify the number of terms and the coefficients of each term.

1. **Identify the terms**:
   - The expression consists of three distinct terms:
     - The first term is $$ x $$.
     - The second term is $$ 4x^{2} $$.
     - The third term is $$ 5x^{3} $$.

2. **Identify the coefficients**:
   - The coefficient of the first term $$ x $$ is $$ 1 $$ (since $$ x $$ can be written as $$ 1x $$).
   - The coefficient of the second term $$ 4x^{2} $$ is $$ 4 $$.
   - The coefficient of the third term $$ 5x^{3} $$ is $$ 5 $$.

3. **Count the number of terms**:
   - There are a total of three terms in the expression.

Now, we can fill in the answer based on the choices provided:

**Choice A**: There are three terms. The coefficient of the first term is $$ 1 $$, the coefficient of the second term is $$ 4 $$, and the coefficient of the third term is $$ 5 $$.

Thus, the correct choice is A, and the filled answer is:
- The coefficient of the first term is $$ 1 $$.
- The coefficient of the second term is $$ 4 $$.
- The coefficient of the third term is $$ 5 $$.
There are three terms. The coefficients are 1, 4, and 5.

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