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Question

Factorise each of the following algebraic expressions:
i) 3x+15 ii) 2x2+5x iii) 3x2y6xy2

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Solution

(i) The greatest common factor of the terms namely, 3x and 15 of the expression 3x + 15 is 3. Also, 3x = 3 × x and 15 = 3×5.
3x+15=3(x+5)
(ii) 2x2=2x×x and 5x=5×x.
2x2+5x=2x×x+5×x=(2x+5)x
(iii) Clearly, 3xy is the greatest common factor of the terms 3x2y and 6xy2 of the binomial
3x2y6xy2.
Also,3x2y=3xy×x and 6xy2=3xy×2y
3x2y6xy2=3xy×x3xy×2y=3xy(x2y)

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