83477
AssignmentMultiple Choice

Factoring Polynomials: Difference of Squares

Question 83477 • FL-1200700-Mathematics for College Algebra MIS

Analyze Cecile’s work. Is it correct?

Answer
A
No, adding in 0x keeps an equivalent polynomial.
B
No, she did not fill in the X correctly. She should have 16 on top and –9 on the bottom.
C
No, 16x6 + 12x3 – 12x3 – 9 is not equivalent to 16x6 – 9.
D
Yes, Cecile factored the polynomial correctly.

Explanation

The polynomial 16x⁶ − 9 is a difference of squares: (4x³)² − 3². Using a² − b² = (a + b)(a − b), it factors as (4x³ + 3)(4x³ − 3). Expanding gives 16x⁶ − 9, so Cecile factored it correctly.

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