Factoring Review

Front

What is factoring in algebra?

Back

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

Front

What is a trinomial?

Back

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

Front

How do you factor a trinomial of the form x^2 + bx + c?

Back

To factor a trinomial of the form x^2 + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are those two numbers.

Front

What is the greatest common factor (GCF)?

Back

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

Front

How do you find the GCF of x^5y^2 and x^2y^7z?

Back

Identify the lowest power of each variable in the terms: GCF = x^2y^2.

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).

Front

Factor the expression x^2 - 9.

Back

(x + 3)(x - 3) because it is a difference of squares.

Front

What does DOTS stand for in factoring?

Back

DOTS stands for Difference of Two Squares, a method used to factor expressions like a^2 - b^2.

Front

Factor the expression 81m^2 - 1.

Back

(9m - 1)(9m + 1) using the difference of squares.

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.