Question

identify the following terms in these three polynomial
leading coefficients color red degree color yellow constant - color green
underline trinomials circle binomials
3x^2 - 9x + 4 - 9x^3 - 4x^2 + 6x + 19 2x^3 - 9
4x^3 - 4x + 10 6x^3 - 1000

Explanation:

Step1: Recall polynomial definitions

A polynomial in one - variable $x$ is of the form $a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0$, where $a_n
eq0$, $n$ is a non - negative integer. The leading coefficient is $a_n$, the degree is $n$, and the constant term is $a_0$. A binomial has two terms and a trinomial has three terms.

Step2: Analyze $3x^2-9x + 4$

Leading coefficient: $3$ (red), Degree: $2$ (yellow), Constant: $4$ (green), It is a trinomial (underline it).

Step3: Analyze $-9x^3-4x^2 + 6x+19$

Leading coefficient: $-9$ (red), Degree: $3$ (yellow), Constant: $19$ (green), It is a polynomial with 4 terms.

Step4: Analyze $2x^3-9$

Leading coefficient: $2$ (red), Degree: $3$ (yellow), Constant: $-9$ (green), It is a binomial (circle it).

Step5: Analyze $4x^3-4x + 10$

Leading coefficient: $4$ (red), Degree: $3$ (yellow), Constant: $10$ (green), It is a trinomial (underline it).

Step6: Analyze $6x^3-1000$

Leading coefficient: $6$ (red), Degree: $3$ (yellow), Constant: $-1000$ (green), It is a binomial (circle it).

Answer:

For $3x^2-9x + 4$: Leading coefficient $3$ (red), Degree $2$ (yellow), Constant $4$ (green), Underlined (trinomial).
For $-9x^3-4x^2 + 6x+19$: Leading coefficient $-9$ (red), Degree $3$ (yellow), Constant $19$ (green).
For $2x^3-9$: Leading coefficient $2$ (red), Degree $3$ (yellow), Constant $-9$ (green), Circled (binomial).
For $4x^3-4x + 10$: Leading coefficient $4$ (red), Degree $3$ (yellow), Constant $10$ (green), Underlined (trinomial).
For $6x^3-1000$: Leading coefficient $6$ (red), Degree $3$ (yellow), Constant $-1000$ (green), Circled (binomial).