Factoring+Expressions

Students are confusing factoring monomials with factoring expressions.

Students are able to factor monomials such as: 36x2y2 as 2 * 2* 3 * 3 * x * x * y * y Then when asked to factor the expression 20a + 4 students answer the question as 2 * 2 * 5 * a + 2 * 2


 * Re-mediation:**Review with students the definition of a monomial: a monomial is a number, a variable, and a product of numbers and/or variables.Then review the definition of an algebraic expression: an expressions is a combination of algebraic terms that do not include an equal sign.

Ask students the question: [|Distributive Property] allow you to do? Answer: Distribute a number that is outside of parentheses to all the terms inside the parentheses to simplify the expression. example 5(x + 4) using the distributive property is 5x + 20. Have students explain each step in the distributive property. Then ask what would you do to 5x + 20 to get it back to 5(x + 4)? Ask the students what the greatest common factor of 5x and 20 is? If necessary factor each term completely. - the greatest common factor is 5 so we divide each term by 5 to know what will be inside the parentheses. The greatest common factor is written outside of the parentheses.To use the distributive property we multiple every term in the parentheses by the number outside of the parentheses. To factor you divide each term in the expression by the GCF.