Multiplying Polynomials by Monomials and Binomials

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables (e.g., 5x^2, -3, 7xy).

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, which can be separated by a plus or minus sign (e.g., x + 2, 3x^2 - 4).

Front

How do you multiply a monomial by a polynomial?

Back

To multiply a monomial by a polynomial, distribute the monomial to each term of the polynomial and combine like terms if necessary.

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

Multiply: -5x^6(3x^2 - 12x + 30)

Back

-15x^8 + 60x^7 - 150x^6.

Front

Multiply: 3x^3(2x^2 + 9x + 6)

Back

6x^5 + 27x^4 + 18x^3.

Front

What is the result of multiplying two binomials?

Back

The result of multiplying two binomials is a polynomial, which can be found using the distributive property or the FOIL method.

Front

Multiply: (x - 3)(x^2 + 2x + 7)

Back

x^3 - x^2 + x - 21.

Front

Multiply: (2x + 3)(x^2 + 4x + 1)

Back

2x^3 + 11x^2 + 14x + 3.

Front

Multiply: 10x(2x^2 + 3x + 4)

Back

20x^3 + 30x^2 + 40x.