Multiplying Polynomials

Front

What is a polynomial?

Back

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

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to combine each term in one polynomial with each term in the other polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a sum.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the FOIL method: First, Outer, Inner, Last to combine the terms.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials, where you multiply the First terms, the Outer terms, the Inner terms, and the Last terms, then combine like terms.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial, representing how many times the variable is multiplied.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined by addition or subtraction.

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.

Front

How do you identify the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in the polynomial.

Front

What is the result of multiplying (x + a)(x + b)?

Back

The result is x^2 + (a + b)x + ab, which is derived using the distributive property.