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Question

Simplify the following polynomials in the simplest form:
1x2+3x+2+1x2+5x+62x2+4x+3

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Solution

The given expression 1x2+3x+2+1x2+5x+62x2+4x+3can be simplified as shown below:

=1x2+3x+2+1x2+5x+62x2+4x+3

=[1x2+3x+2+1x2+5x+6]2x2+4x+3

=[1x2+x+2x+2+1x2+3x+2x+6]2x2+x+3x+3

=[1x(x+1)+2(x+1)+1x(x+3)+2(x+3)]2x(x+1)+3(x+1)

=[1(x+2)(x+1)+1(x+2)(x+3)]2(x+3)(x+1)

=[(x+3)(x+1)(x+2)(x+3)+(x+1)(x+1)(x+2)(x+3)]2(x+1)(x+2)(x+3)(TakingLCM)

=[2x+4(x+1)(x+2)(x+3)]2(x+1)(x+2)(x+3)

=[2(x+2)(x+1)(x+2)(x+3)]2(x+1)(x+2)(x+3)

=2(x+1)(x+2)(x+3)2(x+1)(x+2)(x+3)

=0

Hence, 1x2+3x+2+1x2+5x+62x2+4x+3=0.

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