A fourth degree polynomial will have up to four distinct zeroes, and your description of the problem describes them all. That leaves only one possible area for "wiggle room": the dilation factor "a"
y = (a)(x - 2)(x - 2)(x + 4)(x - 6)
The above polynomial will be a 4th degree polynomial (because 4 "x" terms are multiplied by one another), and will have a value of zero at 2 (twice), -4, and 6 no matter what value the constant "a" takes on.
Notice that the problem asks you to find "a possible formula", not "the formula", therefore the person asking the question will accept any formula that meets the criteria laid out in the question... in other words, you are free to choose whatever value for "a" you wish to use, as no matter what value you assign to "a", the above equation is guaranteed to have those four zeroes and be a 4th degree polynomial.
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A fourth degree polynomial will have up to four distinct zeroes, and your description of the problem describes them all. That leaves only one possible area for "wiggle room": the dilation factor "a"
y = (a)(x - 2)(x - 2)(x + 4)(x - 6)
The above polynomial will be a 4th degree polynomial (because 4 "x" terms are multiplied by one another), and will have a value of zero at 2 (twice), -4, and 6 no matter what value the constant "a" takes on.
Notice that the problem asks you to find "a possible formula", not "the formula", therefore the person asking the question will accept any formula that meets the criteria laid out in the question... in other words, you are free to choose whatever value for "a" you wish to use, as no matter what value you assign to "a", the above equation is guaranteed to have those four zeroes and be a 4th degree polynomial.