Answer :
To determine the missing exponent on the \( x \)-term for the expression \( 5x^2 y^3 + x y^2 + 8 \) to be a trinomial with a degree of 5, we need to ensure that the highest sum of exponents in one of the terms is 5. Let's analyze the provided expression term-by-term.
1. The first term is \( 5x^2 y^3 \):
- The exponents for \( x \) and \( y \) are 2 and 3, respectively.
- Summing these exponents: \( 2 + 3 = 5 \).
- This term already has a degree of 5.
2. The second term is \( x y^2 \):
- Currently, the exponents are 1 for \( x \) and 2 for \( y \).
- Summing these exponents: \( 1 + 2 = 3 \).
To achieve a degree of 5 with this term, we need to adjust the exponent of \( x \) so that the total sum of exponents becomes 5. Denote the missing exponent on \( x \) by \( a \).
[tex]\[ a + 2 = 5 \][/tex]
Solving for \( a \):
[tex]\[ a = 5 - 2 \][/tex]
[tex]\[ a = 3 \][/tex]
Therefore, the missing exponent on the [tex]\( x \)[/tex]-term must be [tex]\( 3 \)[/tex] for the expression to be a trinomial with a degree of 5.
1. The first term is \( 5x^2 y^3 \):
- The exponents for \( x \) and \( y \) are 2 and 3, respectively.
- Summing these exponents: \( 2 + 3 = 5 \).
- This term already has a degree of 5.
2. The second term is \( x y^2 \):
- Currently, the exponents are 1 for \( x \) and 2 for \( y \).
- Summing these exponents: \( 1 + 2 = 3 \).
To achieve a degree of 5 with this term, we need to adjust the exponent of \( x \) so that the total sum of exponents becomes 5. Denote the missing exponent on \( x \) by \( a \).
[tex]\[ a + 2 = 5 \][/tex]
Solving for \( a \):
[tex]\[ a = 5 - 2 \][/tex]
[tex]\[ a = 3 \][/tex]
Therefore, the missing exponent on the [tex]\( x \)[/tex]-term must be [tex]\( 3 \)[/tex] for the expression to be a trinomial with a degree of 5.
