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AP EAMCET202317 May 2023Morning ShiftMathematicsBinomial TheoremActual

The degree of the polynomial (x+ x^4-1 )^9+ (x- x^4-1 )^9 is

Options

  1. A14
  2. B15
  3. C16
  4. D17

Correct answer

D. 17

Step-by-step solution

aligned & (x+ x^4-1 )^9+ (x- x^4-1 )^9 & Let y= x^4-1 y^2=x^4-1 & =(x+y)^9+(x-y)^9 & =2 [ ^9 C₁ x^1 y^8+ ^9 C₃ x^3 y^6+ ^9 C₅ x^5 y^4+ ^9 C₇ x^7 y^2+ ^9 C₉ x^7 y^0 ] & =2 [ ^9 C₁ x^1 (x^4-1 )^4+ ^9 C₃ x^3 (x^4-1 )^3+ ^9 C₄ x^5 (x^4-1 )^2 . & . + ^9 C₇ x^7 (x^4-1 )+ ^9 C₉ x^7 ] & Degree of polynomial =1+4 4=17 aligned

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