Factorise:

2x²+7x+3

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Solution

2x² + 7x + 3 2x² + 7x + 3 1. Multiply the blue 2 by the red 3, getting 6. 2. Think of two positive integers which have product 6 and which have SUM (since the purple sign is +) equal to the green 7. Such positive integers are 1 and 6 because 1×6 = 6 and 1+6 = 7 3. Rewrite the green 7 using 1 and 6 2x² + (1 + 6)x + 3 4. Remove the parentheses using the distributive principle. 2x² + 1x + 6x + 3 5. Factor x out of the first two terms and factor 3 out of the last two terms: x(2x + 1) + 3(2x + 1) 6. Factor the (2x + 1) out of both terms (2x + 1)(x + 3)

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