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Question

Factorize each of the following quadratic polynomials by using the method of completing the square:
4y2 + 12y + 5

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Solution

4y2+12y+5=4(y2+3y+54) [Making the coefficient of y2=1]=4[y2+3y+322-322+54] [Adding and subtracting 322]=4[(y+32)2-94+54]=4[(y+32)2-12] [Completing the square]=4[(y+32)-1][(y+32)+1]=4(y+32-1)(y+32+1)=4(y+12)(y+52)=(2y+1)(2y+5)

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