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QuizMultiple Choice

Factoring with the Binomial Theorem

Question 2 • FL-1202340-Pre-Calculus Honors A

Which statement explains why the polynomial cannot be factored using the binomial theorem?x3 – 4x2 + 16x – 64

Answer
A
The signs do not follow the right pattern.
B
The first and last terms are not perfect cubes.
C
The exponents on each term do not follow the pattern for a binomial expansion.
D
The middle terms do not take into account the coefficients from Pascal’s triangle.

Explanation

A binomial cube such as (x − 4)³ has coefficients 1, 3, 3, 1 from Pascal’s triangle, giving x³ − 12x² + 48x − 64. The given polynomial has middle coefficients −4 and 16 instead, so its middle terms do not match the coefficients required by the binomial theorem. Therefore, the correct statement is that the middle terms do not take into account Pascal’s triangle coefficients.

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