Polynomials- Solving Equations, Division, Function Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x - c).

Front

How do you find the product of two functions f(x) and g(x)?

Back

To find the product of two functions, multiply their expressions: (f ⋅ g)(x) = f(x) * g(x).

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you solve a polynomial equation?

Back

To solve a polynomial equation, set the polynomial equal to zero and find the values of the variable that satisfy the equation.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the remainder theorem?

Back

The remainder theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

How do you perform polynomial long division?

Back

Polynomial long division involves dividing the leading term of the dividend by the leading term of the divisor, then multiplying and subtracting until the remainder is of lower degree.