Completely Factoring Polynomials

Front

What is a polynomial?

Back

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

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the difference between a monomial, binomial, and trinomial?

Back

A monomial has one term, a binomial has two terms, and a trinomial has three terms.

Front

What is the Factor Theorem?

Back

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

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c).

Front

How do you factor a quadratic polynomial?

Back

To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b).

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What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as a^2 + 2ab + b^2 = (a + b)^2.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that divides two or more numbers or terms.