Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What does GCF stand for in polynomial factoring?

Back

GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, first identify and factor out the GCF, then apply other factoring techniques such as grouping, difference of squares, or trinomial factoring.

Front

What is the difference of squares?

Back

The difference of squares is a factoring technique used for expressions in the form a² - b², which can be factored as (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

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 find the degree of a monomial?

Back

To find the degree of a monomial, add the exponents of all the variables in the term.

Front

What is the factored form of x^4 - 9x^2?

Back

The factored form is x^2(x + 3)(x - 3).

Front

What is the first step in factoring the polynomial 2n^2 - 8n^3?

Back

The first step is to factor out the GCF, which is 2n^2, resulting in 2n^2(1 - 4n).

Front

What is a trinomial?

Back

A trinomial is a polynomial with three terms, typically in the form ax^2 + bx + c.

Front

What is the purpose of factoring polynomials?

Back

Factoring polynomials simplifies expressions, makes solving equations easier, and helps in graphing polynomial functions.