Unit 4 Test Review - Polynomials and Factoring

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 expression.

Front

How do you simplify the expression (-10a^4 - 7a^2 + 11) - (9 + 10a^2 - 5a^4)?

Back

To simplify, combine like terms: -10a^4 + 5a^4 - 7a^2 - 10a^2 + 11 - 9 = -5a^4 - 17a^2 + 2.

Front

What is the difference of cubes formula?

Back

The difference of cubes formula states that a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a common factor in all terms.

Front

How do you factor the expression 2x^3 + 5x^2 - 8x - 20 completely?

Back

To factor completely, group the terms: (2x^3 + 5x^2) + (-8x - 20) = x^2(2x + 5) - 4(2x + 5) = (x - 2)(x + 2)(2x + 5).

Front

What is the result of factoring x^3 - 27?

Back

Factoring x^3 - 27 gives (x - 3)(x^2 + 3x + 9) using the difference of cubes formula.

Front

What are like terms in a polynomial?

Back

Like terms are terms that have the same variable raised to the same power.

Front

What is the process of combining like terms?

Back

Combining like terms involves adding or subtracting the coefficients of terms that have the same variable and exponent.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree and determines the end behavior of the polynomial graph.