Question

1. By how many does
$5x ^{5} + 8x^{4} + 4x ^{3} +5x ^{2} + 2x + 8 \: exceed \: 2x ^{5} + 4x ^{4} - 2x ^{3} + 2x ^{2} - x +5$
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Answer 1

Let the number be exceeded by y

=> (2x^5 + 4x^4) + y = 5x^5 + 8x^4 + 4x^3 + 5x^2 + 2x + 8
=> y = 5x^5 + 8x^4 + 4x^3 + 5x^2 + 2x + 8 - (2x^5 + 4x^4)
=> y = 3x^5 + 4x^4 + 4x^3 + 5x^2 + 2x + 8

The answer is 3x^5 + 4x^4 + 4x^3 + 5x^2 + 2x + 8