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Question

Simplify the following two polynomials in the simplest form: 2x25x+3x23x+22x27x42x23x2

A
x+1x2
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B
x1x2
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C
x+1x+2
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D
None of these
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Solution

The correct option is A x+1x2
The given expression 2x25x+3x23x+22x27x42x23x2can be simplified as shown below:

=2x25x+3x23x+22x27x42x23x2

=2x22x3x+3x2x2x+22x28x+x42x24x+x2

=2x(x1)3(x1)x(x1)2(x1)2x(x4)+1(x4)2x(x2)+1(x2)

=(2x3)(x1)(x2)(x1)(2x+1)(x4)(2x+1)(x2)

=2x3x2x4x2

=(2x3)(x4)x2

=2x3x+4x2

=x+1x2

Hence, 2x25x+3x23x+22x27x42x23x2=x+1x2.

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