pre-assessment and after polynomial review

Front

What is the distributive property in algebra?

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 (3x - 5)(4x^2 - 2x - 3)?

Back

To simplify, apply the distributive property: 3x * 4x^2 + 3x * (-2x) + 3x * (-3) - 5 * 4x^2 - 5 * (-2x) - 5 * (-3) = 12x^3 - 6x^2 - 9x - 20x^2 + 10x + 15 = 12x^3 - 26x^2 + x + 15.

Front

What are the steps to factor a quadratic expression like k^2 - 2k - 24?

Back

1. Identify two numbers that multiply to -24 (the constant term) and add to -2 (the coefficient of k). 2. The numbers are 4 and -6. 3. Write the factors as (k + 4)(k - 6).

Front

What is the product of (3x - 1)(x + 5)?

Back

To find the product, use the distributive property: 3x * x + 3x * 5 - 1 * x - 1 * 5 = 3x^2 + 15x - x - 5 = 3x^2 + 14x - 5.

Front

How do you simplify the expression (6b^3 + 6 - b^4) - (8b^3 - 6b^4 + 2)?

Back

Combine like terms: (6b^3 - 8b^3) + (6 + 2) + (-b^4 + 6b^4) = -2b^3 + 8 + 5b^4 = 5b^4 - 2b^3 + 4.

Front

What is the process for simplifying the expression x^3(2x^2 + 3x)?

Back

Distribute x^3 to each term inside the parentheses: x^3 * 2x^2 + x^3 * 3x = 2x^5 + 3x^4.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to whole number exponents and coefficients, 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 expression.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which can be simpler polynomials.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.