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 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 simplify the expression -3x²(7x² - x + 4)?

Back

To simplify, distribute -3x² to each term: -3x² * 7x² = -21x⁴, -3x² * -x = 3x³, -3x² * 4 = -12x². The result is -21x⁴ + 3x³ - 12x².

Front

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

Back

Using the difference of squares formula, the result is 4x² - 9.

Front

What is the formula for the difference of squares?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

How do you expand (x - 3)(x² + 2x + 7)?

Back

Distribute x to each term in (x² + 2x + 7) and then distribute -3 to each term: x³ + 2x² + 7x - 3x² - 6x - 21, which simplifies to x³ - x² + x - 21.

Front

What is the result of multiplying (5x + 2)(x² - 3x + 6)?

Back

Distributing gives: 5x * x² + 5x * -3x + 5x * 6 + 2 * x² + 2 * -3x + 2 * 6, which simplifies to 5x³ - 13x² + 24x + 12.

Front

What is the degree of a polynomial?

Back

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

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor that multiplies a variable in a term of a polynomial.