4.4 Factoring Higher Degree Polynomials

Front

What is the definition of factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

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 factor a polynomial completely?

Back

To factor a polynomial completely means to express it as a product of irreducible polynomials, meaning it cannot be factored further over the given number system.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms.

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.

Tags

CCSS.HSA.APR.B.2

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c).

Tags

CCSS.HSA.APR.B.2

Front

How do you factor a sum of cubes?

Back

A sum of cubes can be factored using the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a difference of cubes?

Back

A difference of cubes can be factored using the formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Tags

CCSS.HSA.APR.C.4

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for a greatest common factor (GCF) among the terms.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Tags

CCSS.HSA.APR.D.6