Synthetic and Long Division Test! Trivia Quiz

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The remainder theorem allows you to evaluate a function at a given value of x by using synthetic division. In synthetic division, the given value of x is used as the divisor, and the resulting remainder is obtained. Therefore, the correct answer is "remainder."

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When dividing any number by itself, the result is always 1. In this case, when dividing -25 by -25, the constant in the answer is indeed -25.

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Synthetic division can only be used when dividing a polynomial by a linear factor of the form (x - a). It cannot be used for dividing polynomials by factors that are not linear. Therefore, the statement that synthetic division can always be used when dividing polynomials is false.

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When dividing a polynomial of degree 6 by a polynomial of degree 2, the quotient will not always be a polynomial of degree 3. The degree of the quotient depends on the degree of the dividend and the divisor. In this case, since the dividend has a degree of 6 and the divisor has a degree of 2, the quotient can have a degree of either 4 or 5, but not 3. Therefore, the statement is false.

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