To determine the missing exponent on the [tex]\( x \)[/tex]-term in the given expression [tex]\( 5x^2 y^3 + xy^2 + 8 \)[/tex] for it to be a trinomial with a degree of 5, follow these steps:
1. Identify the degree of each term:
- For the term [tex]\( 5x^2 y^3 \)[/tex]:
- The exponent of [tex]\( x \)[/tex] is 2.
- The exponent of [tex]\( y \)[/tex] is 3.
- The degree of this term is [tex]\( 2 + 3 = 5 \)[/tex].
- For the term [tex]\( xy^2 \)[/tex]:
- The exponent of [tex]\( x \)[/tex] is 1.
- The exponent of [tex]\( y \)[/tex] is 2.
- The degree of this term is [tex]\( 1 + 2 = 3 \)[/tex].
- For the constant term [tex]\( 8 \)[/tex]:
- A constant term has a degree of 0 because there are no variables with exponents.
2. Determine the highest degree in the expression:
- The highest degree present among the terms is 5, which comes from the term [tex]\( 5x^2 y^3 \)[/tex].
3. Identify the term that determines the expression's degree:
- The term [tex]\( 5x^2 y^3 \)[/tex] determines the degree of the expression because it has the highest degree (which is 5).
4. Check the missing exponent in [tex]\( x \)[/tex]:
- The term [tex]\( 5x^2 y^3 \)[/tex] already has the highest degree (5) in the expression.
- It contains [tex]\( x^2 \)[/tex], where the exponent for [tex]\( x \)[/tex] is 2.
So, the missing exponent on the [tex]\( x \)[/tex]-term in the expression [tex]\( 5x^2 y^3 + xy^2 + 8 \)[/tex] for it to be a trinomial with a degree of 5 is [tex]\( \boxed{2} \)[/tex].
Therefore, there is no need for a new term or changing existing terms since the highest degree is already present in the term [tex]\( 5x^2 y^3 \)[/tex].
