Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What is the degree of a polynomial?

Back

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

Front

What is the Box method in multiplying polynomials?

Back

The Box method is a visual technique used to multiply polynomials by organizing the terms in a grid or box format, making it easier to combine like terms.

Front

How do you set up the Box method for (2x + 1)(x^2 + 3x - 1)?

Back

Write the terms of the first binomial (2x and 1) along the top and the terms of the second polynomial (x^2, 3x, and -1) along the side of the box.

Front

What is the result of multiplying (2x + 1)(x^2 + 3x - 1) using the Box method?

Back

The result is 2x^3 + 7x^2 + x - 1.

Front

How many individual multiplications are performed in the Box method for a binomial times a trinomial?

Back

Six individual multiplications are performed.

Front

What is the combined middle term when using the Box method for (2x + 1)(x - 5)?

Back

The combined middle term is -9x.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials, standing for First, Outside, Inside, Last, which refers to the order of multiplication.

Front

What is the difference between the FOIL method and the Box method?

Back

The FOIL method is a shortcut for multiplying two binomials, while the Box method can be used for multiplying polynomials of any degree and is more visual.

Front

What are like terms in polynomials?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.