5.4 Do Now: Factor completely.5.4 Do Now: Factor completely.1.) x1.) x33 – 7x – 7x22 + 10x + 10x

Algebra II ElementsAlgebra II Elements5.4: Factoring Polynomials5.4: Factoring Polynomials

HW tomorrow: p.357 (10-28 even)HW tomorrow: p.357 (10-28 even)

Test 5.1-5.4: Thursday, 12/11Test 5.1-5.4: Thursday, 12/11

Factor by groupingFactor by grouping1.) x1.) x33 – 3x – 3x22 + 16x – 48 + 16x – 48

2.) y2.) y33 + 5y + 5y22 – 9y – 45 – 9y – 45

Factor by groupingFactor by grouping3.) x3.) x33 – 2x – 2x22 + 3x – 6 + 3x – 6

4.)4.) x x44 + x + x33 + 4x + 4 + 4x + 4

Do Now: FactorDo Now: Factor2x2x88 + 10x + 10x55 + 12x + 12x22

Algebra II ElementsAlgebra II Elements5.4: Factoring Polynomials5.4: Factoring Polynomials

HW: p.357 (10-28 even)HW: p.357 (10-28 even)

Test 5.1-5.4: Thursday, 12/11Test 5.1-5.4: Thursday, 12/11

Factoring CubesFactoring Cubes Sum of Two CubesSum of Two Cubes

aa33 + b + b33 = (a + b)(a = (a + b)(a22 – a b + b – a b + b22))

Difference of Two CubesDifference of Two Cubes

aa33 – b – b33 = (a – b)(a = (a – b)(a22 + a b + b + a b + b22))

Factoring CubesFactoring Cubes Sum of Two CubesSum of Two Cubes

aa33 + b + b33 = (a + b)(a = (a + b)(a22 – ab + b – ab + b22)) Difference of Two CubesDifference of Two Cubes

aa33 – b – b33 = (a – b)(a = (a – b)(a22 + ab + b + ab + b22))

Examples: FactorExamples: Factor

1.) 8x1.) 8x33 + 64 + 64

FactorFactor1.) 64x1.) 64x33 – 27 – 27

2.) x2.) x44 – 36 – 36

FactorFactor3.) 125x3.) 125x33 – 1 – 1

4.) 54x4.) 54x33 – 128 – 128

Algebra II ElementsAlgebra II Elements5.4: Factoring Polynomials5.4: Factoring Polynomials

HW: p.357 (32-50 even)HW: p.357 (32-50 even)

Test 5.1-5.4: Thursday, 12/11Test 5.1-5.4: Thursday, 12/11

FactoringFactoring GCF – always check for a GCF first.GCF – always check for a GCF first. Trinomial (3-terms): traditional 2 Trinomial (3-terms): traditional 2

parenthesis factoring or change to parenthesis factoring or change to grouping.grouping.

Four term polynomial: factor by grouping.Four term polynomial: factor by grouping. Difference of squaresDifference of squares

Cannot factor sum of squaresCannot factor sum of squares Sum or Difference of cubesSum or Difference of cubes

Solve the equation.Solve the equation.1.) 3x1.) 3x55 + 15x = 18x + 15x = 18x33

5.4: Do Now5.4: Do Now For each polynomial expression in the table below,

classify the expression as a difference of squares, difference of cubes, sum of cubes, or none of these by placing a check mark in all appropriate boxes. Then factor each polynomial completely in the space provided below the table.

a. x12 – y6 b. 8x3 + 24y c. x3 + 1

ExpressionDifference of Squares

Difference of Cubes

Sum of Cubes

None of these

a. x12 – y6        b. 8x3 + 24y        

c. x3 + 1        

Solve the equation.Solve the equation.2.) 2.) 4x4x55 – 40x – 40x33 + 36x = 0 + 36x = 0

Solve the equation.Solve the equation.3.) -27x3.) -27x33 + 15x + 15x22 = -6x = -6x44