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Is the function p(x)=2x4−3x2+6p(x) = 2x^4 - 3x^2 + 6 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither

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Full solution

Q. Is the function p(x)=2x4−3x2+6p(x) = 2x^4 - 3x^2 + 6 even, odd, or neither?\newlineChoices:\newline(A)even\newline(B)odd\newline(C)neither
  1. Check Even Function: Check if p(x)p(x) is even by substituting −x-x for xx and comparing p(−x)p(-x) to p(x)p(x).p(−x)=2(−x)4−3(−x)2+6p(-x) = 2(-x)^4 - 3(-x)^2 + 6
  2. Simplify p(−x)p(-x): Simplify the expression for p(−x)p(-x).p(−x)=2x4−3x2+6p(-x) = 2x^4 - 3x^2 + 6
  3. Compare p(−x)p(-x) with p(x)p(x): Compare p(−x)p(-x) with p(x)p(x).\newlineSince p(−x)=p(x)p(-x) = p(x), the function p(x)p(x) is even.

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