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Operations with Complex Numbers

Question 1 • Fall 24 GMS Advanced Algebra: Concepts and Connections A

What is x2 – 6 = 16x + 30 rewritten in standard form, then factored? | What value(s) of x make the equation true?

Answer
A
(x – 18)(x + 2) = 0
B
(x – 6)(x – 6) = 0
C
(x + 6)(x – 6) = 0
D
(x + 18)(x – 2) = 0

Explanation

Move all terms to one side: x² − 6 = 16x + 30 becomes x² − 16x − 36 = 0. The numbers that multiply to −36 and add to −16 are −18 and 2, so the equation factors as (x − 18)(x + 2) = 0. Thus x = 18 or x = −2, matching choice A.

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