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 is the degree of a polynomial?

Back

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

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degrees.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last.

Front

What does the distributive property state?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

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

Back

The result is x^2 + (a + b)x + ab.

Front

How do you simplify the expression 2x(-2x - 3)?

Back

Distribute 2x to both terms: 2x * -2x = -4x^2 and 2x * -3 = -6x, resulting in -4x^2 - 6x.

Front

What is the result of multiplying (3x - 6)(7x + 7)?

Back

The result is 21x^2 - 21x - 42.

Front

What is the process of dividing a polynomial by a monomial?

Back

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

Front

What is the result of multiplying (x + 5)(x + 4)?

Back

The result is x^2 + 9x + 20.