Question

1. for $3x + 12x^2 + 12x^3$, which of the following statements is true?

a the polynomial is a trinomial.
b the degree of the polynomial is 5.
c the polynomial is in standard form.
d the leading coefficient is 3.

Explanation:

Step1: Analyze Option A

A trinomial is a polynomial with three terms. The given polynomial \(3x + 12x^{2}+12x^{3}\) has three terms: \(3x\), \(12x^{2}\), and \(12x^{3}\). So, it is a trinomial.

Step2: Analyze Option B

The degree of a polynomial is the highest power of the variable. In \(3x + 12x^{2}+12x^{3}\), the highest power of \(x\) is \(3\) (from \(12x^{3}\)), so the degree is \(3\), not \(5\). Thus, option B is false.

Step3: Analyze Option C

A polynomial in standard form is written with the terms in descending order of their degrees. The given polynomial has terms with degrees \(1\), \(2\), and \(3\). To be in standard form, it should be \(12x^{3}+12x^{2}+3x\), so the given polynomial is not in standard form. Thus, option C is false.

Step4: Analyze Option D

The leading coefficient is the coefficient of the term with the highest degree. The term with the highest degree (\(3\)) is \(12x^{3}\), so the leading coefficient is \(12\), not \(3\). Thus, option D is false.

Answer:

A. The polynomial is a trinomial.