Factoring Unit 2 Day 4 review from algebra 1-2

A-SSE.A.2: I can use the structure of an expression to identify ways to rewrite it.

rewrite it by factoring form. Today I will learn to recognize the unique structure of an expression and rewrite it by factoring form.

using the Bottoms Up Method Factoring a Trinomial using the Bottoms Up Method

Guided practice Example 1

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. In this problem no common terms exist. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number. Remember if the # is negative, you will have to look at each set with one number positive and one number negative.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM

Guided practice Example 2

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

Guided practice – Thinking map Example 3

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

INDIVIDUAL practice Example 4

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

Factoring Monomials First

Guided practice Example 5

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

Guided practice Example 6

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

INDIVIDUAL practice Example 7

Bottoms Up Method for Factoring Trinomial Expressions Factoring & Solving Quadratic Equations Step 1: Factor out any common terms. Step 2: Multiply the “a” and “c” Step 3: Look for all pairs of factor for this number.

Step 4: Choose the pair of factors that will equal the “b” term. Step 5: Use this pair to write preliminary factors. Step 6: Divide each pair, selected in step 4, by the leading coefficient, “a” term. Step 7: If possible, reduce the fractions into an integer.

Step 8: If the fraction does not divide evenly, resulting in an integer, then pull divisor up to be the leading coefficient for the x term. FACTORED FORM FACTORED FORM

Checking for understanding… How is factoring polynomials related to multiplication of polynomials?

Checking for understanding… What characteristic would determine if a trinomial could not be factored?