To determine the coefficient of [tex]\( n^3 \)[/tex] in the expression [tex]\( 3n^4 - 5n^3 + 9 \)[/tex], follow these steps:
1. Identify the term containing [tex]\( n^3 \)[/tex]:
- Look at each term in the given expression to find the one that includes [tex]\( n^3 \)[/tex].
- The expression is [tex]\( 3n^4 - 5n^3 + 9 \)[/tex].
2. Examine the terms individually:
- The first term is [tex]\( 3n^4 \)[/tex], which includes [tex]\( n^4 \)[/tex] but not [tex]\( n^3 \)[/tex].
- The second term is [tex]\( -5n^3 \)[/tex], which includes [tex]\( n^3 \)[/tex].
- The third term is [tex]\( 9 \)[/tex], which is a constant and does not include [tex]\( n^3 \)[/tex] at all.
3. Extract the coefficient:
- The term [tex]\( -5n^3 \)[/tex] contains [tex]\( n^3 \)[/tex].
- The coefficient of [tex]\( n^3 \)[/tex] in this term is the number multiplying [tex]\( n^3 \)[/tex], which is [tex]\( -5 \)[/tex].
Therefore, the coefficient of [tex]\( n^3 \)[/tex] in the expression [tex]\( 3n^4 - 5n^3 + 9 \)[/tex] is [tex]\( -5 \)[/tex].
So, the correct answer is:
B. [tex]\(-5\)[/tex]
