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, meaning you can distribute a factor across 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 products of each pair of terms.

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 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 is a degree of a polynomial?

Back

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

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power, which can be combined by adding or subtracting their coefficients.

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 or FOIL method.

Front

How do you simplify the expression (k + 4)(5k - 1)?

Back

Using the distributive property: k*5k + k*(-1) + 4*5k + 4*(-1) = 5k^2 + 19k - 4.