Answer :
Sure! Let's find the coefficient and degree of each polynomial step-by-step.
a) [tex]\(8x^6 + 16x^3 - 7\)[/tex]
1. Identify the degree of the polynomial:
- The degree of a polynomial is the highest power of [tex]\(x\)[/tex] present in the expression.
- In this polynomial, the terms are [tex]\(8x^6\)[/tex], [tex]\(16x^3\)[/tex], and [tex]\(-7\)[/tex].
- The highest power of [tex]\(x\)[/tex] is [tex]\(6\)[/tex] in the term [tex]\(8x^6\)[/tex].
2. Identify the coefficient of the term with the highest degree:
- Look at the term with the highest degree, which is [tex]\(8x^6\)[/tex].
- The coefficient of this term is [tex]\(8\)[/tex].
So for the polynomial [tex]\(8x^6 + 16x^3 - 7\)[/tex], the coefficient of the highest degree term is [tex]\(8\)[/tex], and the degree is [tex]\(6\)[/tex].
b) [tex]\(12x^3 + 50\)[/tex]
1. Identify the degree of the polynomial:
- Again, the degree is the highest power of [tex]\(x\)[/tex].
- In this polynomial, the terms are [tex]\(12x^3\)[/tex] and [tex]\(50\)[/tex].
- The highest power of [tex]\(x\)[/tex] is [tex]\(3\)[/tex] in the term [tex]\(12x^3\)[/tex].
2. Identify the coefficient of the term with the highest degree:
- Look at the term with the highest degree, which is [tex]\(12x^3\)[/tex].
- The coefficient of this term is [tex]\(12\)[/tex].
So for the polynomial [tex]\(12x^3 + 50\)[/tex], the coefficient of the highest degree term is [tex]\(12\)[/tex], and the degree is [tex]\(3\)[/tex].
To summarize:
- For [tex]\(8x^6 + 16x^3 - 7\)[/tex], the coefficient is [tex]\(8\)[/tex] and the degree is [tex]\(6\)[/tex].
- For [tex]\(12x^3 + 50\)[/tex], the coefficient is [tex]\(12\)[/tex] and the degree is [tex]\(3\)[/tex].
a) [tex]\(8x^6 + 16x^3 - 7\)[/tex]
1. Identify the degree of the polynomial:
- The degree of a polynomial is the highest power of [tex]\(x\)[/tex] present in the expression.
- In this polynomial, the terms are [tex]\(8x^6\)[/tex], [tex]\(16x^3\)[/tex], and [tex]\(-7\)[/tex].
- The highest power of [tex]\(x\)[/tex] is [tex]\(6\)[/tex] in the term [tex]\(8x^6\)[/tex].
2. Identify the coefficient of the term with the highest degree:
- Look at the term with the highest degree, which is [tex]\(8x^6\)[/tex].
- The coefficient of this term is [tex]\(8\)[/tex].
So for the polynomial [tex]\(8x^6 + 16x^3 - 7\)[/tex], the coefficient of the highest degree term is [tex]\(8\)[/tex], and the degree is [tex]\(6\)[/tex].
b) [tex]\(12x^3 + 50\)[/tex]
1. Identify the degree of the polynomial:
- Again, the degree is the highest power of [tex]\(x\)[/tex].
- In this polynomial, the terms are [tex]\(12x^3\)[/tex] and [tex]\(50\)[/tex].
- The highest power of [tex]\(x\)[/tex] is [tex]\(3\)[/tex] in the term [tex]\(12x^3\)[/tex].
2. Identify the coefficient of the term with the highest degree:
- Look at the term with the highest degree, which is [tex]\(12x^3\)[/tex].
- The coefficient of this term is [tex]\(12\)[/tex].
So for the polynomial [tex]\(12x^3 + 50\)[/tex], the coefficient of the highest degree term is [tex]\(12\)[/tex], and the degree is [tex]\(3\)[/tex].
To summarize:
- For [tex]\(8x^6 + 16x^3 - 7\)[/tex], the coefficient is [tex]\(8\)[/tex] and the degree is [tex]\(6\)[/tex].
- For [tex]\(12x^3 + 50\)[/tex], the coefficient is [tex]\(12\)[/tex] and the degree is [tex]\(3\)[/tex].
