Question

UNIT 5
Polynomials and Properties of Exponents
LESSON 1
Polynomials

Answer 1

A polynomial is a mathematical expression consisting of variables and coefficients, and is formed by adding or subtracting terms.

For example,

3x^2 + 2x - 5

is a polynomial consisting of three terms. The variable is x, the coefficients are 3, 2, and -5, and the exponents are 2, 1 (which is usually not written explicitly), and 0 respectively.

The degree of a polynomial is the highest exponent present in the expression. In the example above, the degree is 2.

Polynomials can be added or subtracted by combining like terms. For example,

(3x^2 + 2x - 5) + (2x^2 + 3x + 1)

can be simplified by adding the like terms:

= (3x^2 + 2x^2) + (2x + 3x) + (-5 + 1)

= 5x^2 + 5x - 4

Polynomials can also be multiplied, using the distributive property. For example,

(3x^2 + 2x - 5)(2x + 1)

= 6x^3 + 3x^2 + 4x^2 + 2x - 10x - 5

= 6x^3 + 7x^2 - 8x - 5

Polynomials are important in many areas of mathematics, including algebra, calculus, and number theory. They are used to model and solve a wide variety of problems, and have many important properties and applications.