Factoring Polynomials

Front

What is 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 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 completely?

Back

Factoring completely means breaking down a polynomial into its simplest factors, such that no further factoring is possible.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states: a² - b² = (a + b)(a - b).

Tags

CCSS.HSA.APR.C.4

Front

What is the sum of cubes formula?

Back

The sum of cubes can be factored using the formula: a³ + b³ = (a + b)(a² - ab + b²).

Tags

CCSS.HSA.APR.C.4

Front

What is the difference of cubes formula?

Back

The difference of cubes can be factored using the formula: a³ - b³ = (a - b)(a² + ab + b²).

Tags

CCSS.HSA.APR.C.4

Front

How do you factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the role of the greatest common factor (GCF) in factoring?

Back

The GCF is the largest factor that divides all terms in a polynomial. Factoring out the GCF simplifies the polynomial before further factoring.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear binomial, often used to find factors and roots.

Tags

CCSS.HSA.APR.D.6