Polynomial Operations and Factoring Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. For example, 2x^2 + 3x - 5 is a polynomial.

Front

What does GCF stand for in polynomial operations?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides two or more numbers or terms.

Front

What is the difference of two squares?

Back

The difference of two squares is a factoring method used for expressions in the form a^2 - b^2, which can be factored as (a + b)(a - b).

Front

How do you factor the expression x^2 - 36?

Back

The expression x^2 - 36 can be factored using the difference of two squares method as (x + 6)(x - 6).

Front

What is the result of (2x + 6)(2x - 6)?

Back

The result of (2x + 6)(2x - 6) is 4x^2 - 36, using the difference of two squares.

Front

What is the process of combining like terms in polynomials?

Back

Combining like terms involves adding or subtracting coefficients of terms that have the same variable and exponent. For example, 3x + 2x = 5x.

Front

What is the result of subtracting (3 - 2x + 2x^2) - (4x - 5 + 3x^2)?

Back

The result is -x^2 - 6x + 8.

Front

What is the inverse of the points (1,3)(2,4)(6,2)?

Back

The inverse of the points (1,3)(2,4)(6,2) is (3,1)(4,2)(2,6).

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 exponents. For example, 4x^3 + 2x^2 - x + 7.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in finding roots of the polynomial.