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Question

Simplify the following two polynomials in the simplest form: x+2x2+3x+2+x−3x2−2x−3

A
2x+1
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B
2x1
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C
2x+2
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D
None of these
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Solution

The correct option is B 2x+1
The given expression x+2x2+3x+2+x3x22x3can be simplified as shown below:

=x+2x2+3x+2+x3x22x3

=x+2x2+2x+x+2+x3x23x+x3

=x+2x(x+2)+1(x+2)+x3x(x3)+1(x3)

=x+2(x+1)(x+2)+x3(x+1)(x3)

=1(x+1)+1(x+1)

=1+1x+1

=2x+1

Hence, x+2x2+3x+2+x3x22x3=2x+1.

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