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After simplifying (3x^4(x^4-2)-3x^8+11x^6), what is the degree?

Answer and explanation

Correct answer: 6

First expand the expression: \(3x^4(x^4-2)=3x^8-6x^4\). Thus, the polynomial becomes \(3x^8-6x^4-3x^8+11x^6=11x^6-6x^4\). The terms \(3x^8\) and \(-3x^8\) cancel, so the highest remaining exponent is 6. Therefore, the degree is 6; 8 is only visible before simplification. Exam tip: always simplify a polynomial completely before finding its degree.

Related tags

PolynomialsDegree Of PolynomialExpansionLike TermsCancellationDegree Of A PolynomialIntroduction To PolynomialsMathematics

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