Question

unit 1: polynomials

• add/ sub polynomials
• multiply polynomials
• special case multiplying

1. degree of a polynomial is the ______ of the term with the highest exponent.
2. leading coefficient is the ______ of the term with the highest exponent.
3. a polynomial with 1 term is called a ______.
4. a polynomial with 2 terms is called a ______.
5. a polynomial with 3 terms is called a ______.

answer the following questions 6- 9 for

• 7 + 4x⁴ + 2x³

1. what type of polynomial is this polynomial?
2. what is the degree of this polynomial?
3. write the polynomial in standard form.
4. what is the leading coefficient?
5. simplify

(4x³ − 5x² + 3x − 8) − (2x³ − 2x² + 6x + 12) =

1. simplify ( 3x − 8)(2x² + 1)
2. simplify (3x − 4)²

Explanation:

Question 6

A polynomial is classified by the number of terms. The given polynomial \(-7 + 4x^4 + 2x^3\) has three terms: \(-7\), \(4x^4\), and \(2x^3\). A polynomial with three terms is called a trinomial.

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial. In the polynomial \(-7 + 4x^4 + 2x^3\), the terms have exponents 0 (for the constant term \(-7\), since \(x^0 = 1\)), 4 (for \(4x^4\)), and 3 (for \(2x^3\)). The highest exponent is 4.

The standard form of a polynomial is written with the terms in descending order of their exponents. For the polynomial \(-7 + 4x^4 + 2x^3\), we arrange the terms from the highest exponent to the lowest. The term with the highest exponent is \(4x^4\) (exponent 4), then \(2x^3\) (exponent 3), and then the constant term \(-7\) (exponent 0).

Answer:

Trinomial

Question 7