Writing Polynomial Equations

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression that involves a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression. For example, in the polynomial f(x) = 4x^3 + 3x^2 + 2, the degree is 3.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers. For example, 5x^2 is a monomial.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a trinomial?

Back

A trinomial is a polynomial with exactly three terms. For example, x^2 + 3x + 2 is a trinomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when it is written in descending order of the degree of its terms. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

Front

What are the roots of a polynomial?

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero. They can be found by factoring the polynomial or using the quadratic formula for quadratic polynomials.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x). This helps in factoring polynomials.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder of this division is f(c). This can be used to evaluate polynomials quickly.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or synthetic division.