To classify the polynomial expression [tex]\(4x^2 + 3xy + 12yz\)[/tex] by its degree and the number of terms, let's break it down step-by-step.
1. Identifying the terms:
- The given expression has three terms: [tex]\(4x^2\)[/tex], [tex]\(3xy\)[/tex], and [tex]\(12yz\)[/tex].
2. Finding the degree of each term:
- The degree of a term is the sum of the exponents of the variables in that term.
- For [tex]\(4x^2\)[/tex]:
- Exponent of [tex]\(x\)[/tex] is 2.
- The degree is [tex]\(2\)[/tex].
- For [tex]\(3xy\)[/tex]:
- Exponent of [tex]\(x\)[/tex] is 1.
- Exponent of [tex]\(y\)[/tex] is 1.
- The degree is [tex]\(1 + 1 = 2\)[/tex].
- For [tex]\(12yz\)[/tex]:
- Exponent of [tex]\(y\)[/tex] is 1.
- Exponent of [tex]\(z\)[/tex] is 1.
- The degree is [tex]\(1 + 1 = 2\)[/tex].
3. Determining the highest degree:
- Among the terms, [tex]\(4x^2\)[/tex], [tex]\(3xy\)[/tex], and [tex]\(12yz\)[/tex], all have the same degree of [tex]\(2\)[/tex].
- Therefore, the highest degree of the polynomial is [tex]\(2\)[/tex].
4. Counting the number of terms:
- There are 3 terms in the expression: [tex]\(4x^2\)[/tex], [tex]\(3xy\)[/tex], and [tex]\(12yz\)[/tex].
5. Classifying the polynomial:
- A polynomial with three terms is called a trinomial.
- Because the highest degree of the polynomial is [tex]\(2\)[/tex], it is a 2nd degree polynomial.
Therefore, the expression [tex]\(4x^2 + 3xy + 12yz\)[/tex] is classified as a 2nd degree trinomial.
