For the expression [tex]5x^2y^3 + xy^2 + 8[/tex] to be a trinomial with a degree of 5, the missing exponent on the [tex]x[/tex]-term must be:

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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.