Multiplying Polynomials

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 does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in another polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to distribute a term across a sum.

Front

How do you multiply a binomial by a binomial?

Back

To multiply a binomial by a binomial, use the FOIL method: First, Outer, Inner, Last to find the sum of the products.

Front

What is the FOIL method?

Back

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

Front

What are like terms in polynomials?

Back

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

Front

What is the degree of a polynomial?

Back

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

Front

How do you find the product of (2x - 1)(x + 2)?

Back

Use the distributive property or FOIL: 2x*x + 2*(-1) + x*(-1) + 2x*(-1) = 2x^2 + 3x - 2.

Front

What is the result of multiplying (x - 3)(x + 10)?

Back

The result is x^2 + 7x - 30.

Front

What is the result of multiplying (5x + 2)(x^2 - 3x + 6)?

Back

The result is 5x^3 - 13x^2 + 24x + 12.