Answers FL-1202340-Pre-Calculus Honors A Factoring with the Binomial TheoremQuestion 6

6

QuizMultiple Choice

Factoring with the Binomial Theorem

Question 6 • FL-1202340-Pre-Calculus Honors A

Which statement explains why the polynomial cannot be factored using the binomial theorem?125x3 + 900x2 – 2,160x + 1,728

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

The first and last terms are cubes: 125x³ = (5x)³ and 1,728 = 12³. Their cube-binomial coefficients also match: the middle-term magnitudes are 900 and 2,160. But the signs are +, +, −, +, which match neither (5x + 12)³ nor (5x − 12)³, so the signs do not follow the right pattern.

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