Choice A is not the answer because if you expand everything out, you end up with a 7th degree polynomial. The leading terms are x, x^3 and x^3 for each factor, which overall becomes x*x^3*x^3 = x^7. The graph shown is an even function so there is no way that any of the terms have odd exponents. Furthermore, the end behavior suggests that the function has a leading term with an even exponent.

Choice C is not the answer because of similar reasons as choice A. This time the polynomial is a 9th degree polynomial, which is also odd.

Choice D is not the answer because the (x-a)^5 term means that one of the roots cuts through the x axis instead of merely touching it at one point like what is shown in the image

The only thing that is left is choice B. It is an even function and the leading term has an even exponent. Each root has multiplicity that is even so that means each root touches the x axis instead of crossing over.

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4 years ago