14
QuizMultiple Choice

Synthetic Division and the Remainder Theorem — Unit test

Question 14 • FL-1200330-Algebra 2 CR

Which statement best describes the equation x5 + x3 – 14 = 0?

Answer
A
The equation is quadratic in form because it is a fifth-degree polynomial.
B
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2.
C
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
D
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

Explanation

An equation is quadratic in form when its powers can be written as 2n, n, and 0, so a substitution such as u = x^n turns it into a quadratic. Here the powers are 5, 3, and 0; there is no n for which 5 = 2n and 3 = n. Thus it cannot be rewritten as a second-degree polynomial. The fact that the exponents 5 and 3 differ by 2 is not enough to make the equation quadratic in form.

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