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 this form, find two numbers that multiply to c and add to b, then express the trinomial as (x + m)(x + n), where m and n are the 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 two terms?

Back

To find the GCF, identify the common factors of the terms and choose the highest one.

Front

What is the difference of squares?

Back

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

Front

What is a perfect square trinomial?

Back

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

Front

How do you factor by grouping?

Back

To factor by grouping, group terms with common factors, factor out the GCF from each group, and then factor out the common binomial factor.

Front

What is the process to factor a polynomial completely?

Back

To factor a polynomial completely, first factor out the GCF, then look for patterns (like difference of squares or trinomials) and continue factoring until no further factoring is possible.

Front

What is the role of coefficients in factoring?

Back

Coefficients are the numerical factors in a polynomial that can affect the factoring process, especially when finding the GCF or factoring out common terms.