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What is the factored form of 5x − 625x4

Options:
A. 5x(1 + 5x)(1 - 5x + 25x2)
B. 5x(1 - 5x)(1 + 5x + 25x2)
C. (1 - 5x)(1 + 5x + 25x2)
D. (1 + 5x)(1 - 5x + 25x2)

Sagot :

Answer:

B

Step-by-step explanation:

5x - 625[tex]x^{4}[/tex] ← factor out 5x from each term

= 5x(1 - 125x³) ← this factor is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

1 - 125x³

= 1³ - (5x)³

= (1 - 5x) (1² + 5x(1) + (5x)² )

= (1 - 5x) (1 + 5x + 25x²)

Then

5x - 625[tex]x^{4}[/tex] = 5x(1 + 5x + 25x²)

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