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 Trinomials

Mathematics — Second Preparatory

Factoring Trinomials

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Factor x² + 5x + 6	Factor
Solution	We need two numbers whose product is 6 and whose sum is 5. They are 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3). Check: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6	neednumberswhoseproduct
Example 2	Factor x² − x − 12	Factor
Solution	The product is −12 and the sum is −1. The numbers are −4 and 3. So x² − x − 12 = (x − 4)(x + 3). Check: x² + 3x − 4x − 12 = x² − x − 12	productnumbersCheck
Example 3	Factor x² − 7x + 10	Factor
Solution	The product is 10 and the sum is −7. The numbers are −2 and −5. So x² − 7x + 10 = (x − 2)(x − 5)	productnumbers
Example 4	Factor 2x² + 7x + 3	Factor
Solution	The product 2 × 3 = 6 and the two numbers whose product is 6 and sum is 7 are 6 and 1. We write 2x² + 6x + x + 3 = 2x(x + 3) + (x + 3) = (2x + 1)(x + 3). Check: 2x² + 6x + x + 3 = 2x² + 7x + 3	productnumberswhosewrite

Comparison aspect	Main idea	Keywords
Example 5	Factor x² + 2x − 15	Factor
Solution	We need two numbers whose product is −15 and whose sum is 2. They are 5 and −3. So x² + 2x − 15 = (x + 5)(x − 3). Check: x² − 3x + 5x − 15 = x² + 2x − 15	neednumberswhoseproduct

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