18
QuizMultiple Choice

Synthetic Division and the Remainder Theorem — Unit test

Question 18 • FL-1200330-Algebra 2 CR

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

Answer
A
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).
B
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
C
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
D
The equation is not quadratic in form because there is no real solution.

Explanation

Let u = x + 5. Then the equation becomes u² + 4u + 12 = 0, which is a quadratic equation in u, so the original equation is quadratic in form. Expanding it gives a second-degree polynomial, not a fourth-degree one. Although this quadratic has no real solutions, that does not stop it from being quadratic in form.

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