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 greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor out the GCF from a polynomial?

Back

To factor out the GCF, identify the largest common factor of all terms in the polynomial and divide each term by this factor, then write the polynomial as the product of the GCF and the remaining expression.

Front

Factor the polynomial: 39y^5 + 12y^4 - 3y^3

Back

3y^3(13y^2 + 4y - 1)

Front

What is a difference of squares?

Back

A difference of squares is a special factoring pattern that applies to expressions of the form a^2 - b^2, which can be factored as (a - b)(a + b).

Front

Factor the expression: 169 - 9x^2

Back

-1(3x + 13)(3x - 13)

Front

What does it mean if a polynomial is unfactorable?

Back

A polynomial is unfactorable if it cannot be expressed as a product of simpler polynomials with real coefficients.

Front

Factor the polynomial: w^3 + 3w

Back

w(w^2 + 3)

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, from the highest degree to the lowest.