3 Answers:
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Explanation:
The number in the upper left corner of the synthetic division table is the test root we're trying out. If it leads to a remainder of 0 (bottom right corner), then we have a winner. In this case, we have a root. Choice A is one of the answers.
Since 4 is a root, this leads to x-4 being a factor. Think of x = 4 becoming x-4 = 0 when we subtract 4 from both sides. Choice C is another answer.
The remaining stuff in the bottom row forms the quotient polynomial. The coefficients 3 and -1 lead to 3x+(-1) which simplifies to 3x-1.
So this means dividing 3x^2-13x+4 over x-4 yields the quotient 3x-1 with a remainder of 0. Therefore, choice E is the correct equation compared to choice D which is close but not quite there.
