Curriculum

Course: Mathematics — Second Preparatory

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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Factoring by Grouping

Mathematics — Second Preparatory

Factoring by Grouping

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Factor xy + 2x + 3y + 6	Factor
Solution	Group the first two terms and the last two terms: x(y + 2) + 3(y + 2). The common bracket is (y + 2) so the factoring is (x + 3)(y + 2). Check: (x + 3)(y + 2) = xy + 2x + 3y + 6	Groupfirsttermslast
Example 2	Factor x³ + 2x² + 3x + 6	Factor
Solution	The first two terms give x²(x + 2) and the last two terms give 3(x + 2). The common bracket is (x + 2) so the factoring is (x + 2)(x² + 3)	firsttermsgivelast
Example 3	Factor 2ab − 6a + 3b − 9	Factor
Solution	The first group gives 2a(b − 3) and the second group gives 3(b − 3). The common bracket is (b − 3) so the factoring is (b − 3)(2a + 3). Check: 2ab + 3b − 6a − 9	firstgroupgivessecond
Example 4	Factor xy − 3x − 2y + 6	Factor

Comparison aspect	Main idea	Keywords
Solution	The first group gives x(y − 3) and the second group gives −2(y − 3). Note the negative sign when taking out −2. The common bracket is (y − 3) so the factoring is (x − 2)(y − 3). Check: xy − 3x − 2y + 6	firstgroupgivessecond
Example 5	Factor x³ − x² + x − 1	Factor
Solution	Group the first two terms to get x²(x − 1) and group the last two terms to get 1(x − 1). The common bracket is (x − 1) so the factoring is (x − 1)(x² + 1). Check: x³ + x − x² − 1 = x³ − x² + x − 1	Groupfirsttermslast

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