Factoring with the Binomial Theorem

Question 3 • FL-1202340-Pre-Calculus Honors A

What is the factored form of the binomial expansion x4 – 16x3 + 96x2 – 256x + 256?

Answer

(x – 4)4

(x + 4)4

(x – 16)4

(x + 16)4

Explanation

The binomial theorem gives (x − 4)⁴ = x⁴ − 4·4x³ + 6·16x² − 4·64x + 256. Simplifying gives x⁴ − 16x³ + 96x² − 256x + 256, which matches the given expression. Therefore, the factored form is choice A, (x − 4)⁴.

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