Factoring Expressions

Front

What is factoring in algebra?

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 the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that two or more numbers share. It is used in factoring to simplify expressions.

Front

How do you factor the expression 21x - 36?

Back

The expression can be factored by finding the GCF, which is 3. Thus, 21x - 36 = 3(7x - 12).

Front

What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, such that no further factoring is possible.

Front

How can you verify if two expressions are equivalent, such as 2x + 6 and 2(x + 3)?

Back

You can verify equivalence by simplifying both expressions. If they simplify to the same expression, they are equivalent.

Front

What is the factored form of the expression 16 + 24x?

Back

The factored form is 8(2 + 3x), where 8 is the GCF.

Front

How do you factor the expression 4x + 30y?

Back

The expression can be factored by finding the GCF, which is 2. Thus, 4x + 30y = 2(2x + 15y).

Front

What is the factored form of the expression 5x - 25?

Back

The factored form is 5(x - 5), where 5 is the GCF.

Front

What is the difference between factoring and expanding an expression?

Back

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

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.