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
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
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
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