Factoring Algebraic Expressions

Front

What is factoring in algebra?

Back

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

Front

What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor out the greatest common factor (GCF)?

Back

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

Front

Factor the expression: 6a^2b^3 + 9a^3b^2 + 3a^2b^2

Back

3a^2b^2(2b + 3a + 1)

Front

What is the difference between factoring and expanding an expression?

Back

Factoring is breaking down an expression into its factors, while expanding is multiplying out the factors to get the original expression.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means rewriting it as a product of simpler polynomials or monomials.

Front

Factor the expression: 6a^2b + 4ab^2 + 2ab

Back

2ab(3a + 2b + 1)

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms.

Front

Factor the expression: 14a^3b^4 + 6a^3b^2 + 8a^3b^3

Back

2a^3b^2(7b^2 + 3 + 4b)

Front

What is a trinomial?

Back

A trinomial is a polynomial that contains exactly three terms.