4
QuizMultiple Choice

Factoring with the Binomial Theorem

Question 4 • FL-1202340-Pre-Calculus Honors A

Which polynomial can be factored using the binomial theorem?

Answer
A
343x3 – 441x2 + 567x – 729
B
343x3 – 882x2 + 1,134x – 729
C
1,296x4 – 216x3 + 36x2 – 6x + 1
D
1,296x4 – 864x3 + 216x2 – 24x + 1

Explanation

The binomial theorem gives (a − b)^4 = a^4 − 4a^3b + 6a^2b^2 − 4ab^3 + b^4. Substituting a = 6x and b = 1 gives (6x − 1)^4 = 1,296x^4 − 864x^3 + 216x^2 − 24x + 1. Therefore, choice D is the polynomial that factors as a binomial raised to the fourth power.

AI-written and checked against the verified answer.

Previous
Next