A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.
What does it mean to add polynomials?
Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.
How do you subtract polynomials?
To subtract polynomials, distribute the negative sign to the polynomial being subtracted, and then combine like terms.
What is the rule for multiplying monomials?
When multiplying monomials, multiply the coefficients and add the exponents of like bases together.
What happens when you multiply two binomials?
When multiplying two binomials, use the FOIL method: First, Outside, Inside, Last, to multiply each term in one binomial with each term in the other binomial.
How do you divide a polynomial by a monomial?
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial individually.
What is the degree of a polynomial?
The degree of a polynomial is the highest exponent of its terms when the polynomial is expressed in its standard form.
What is the main goal when simplifying a polynomial expression?
The main goal is to combine all like terms to write the polynomial in its simplest form.
Can you combine terms that have different variables in polynomials?
No, you can only combine like terms with the same variables raised to the same powers.
How can you use the distributive property with polynomials?
Use the distributive property to multiply each term in the parenthesis by the term outside the parenthesis.
What is a constant term in a polynomial?
A constant term is a term in a polynomial that does not contain any variables, only a number.
How do you recognize a quadratic polynomial?
A quadratic polynomial is a polynomial of degree 2, which means its highest exponent is 2.
Why is it important to arrange polynomials in standard form before performing operations?
Arranging them helps in easier identification and combination of like terms, making calculations more organized and accurate.
What is the standard form of a polynomial?
The standard form of a polynomial is when its terms are ordered from the highest to the lowest degree.
What does it mean to factor a polynomial?
Factoring a polynomial means writing it as a product of its factors, which can often simplify solving equations involving the polynomial.