3 years ago

What is the factorization of 729x15+1000?

1 answer:

8 0

729x¹⁵ + 1000

This is a case of a sum of cubes.

729 is the cube of 9
1000 is the cube of 10
x¹⁵ is the cube of x⁵

A sum of perfect cubes can be factored into
(a + b) (a² - ab + b²)

(9x⁵+ 10) ((9x⁵)²-(9x⁵)(10) + 10²)

(9x⁵ + 10) (81x¹⁰ - 90x⁵ + 100) THIS IS THE FACTORIZATION

9x⁵ (81x¹⁰ - 90x⁵ + 100) + 10(81x¹⁰ - 90x⁵ + 100)
729x¹⁵ - 810x¹⁰ + 900x⁵ + 810x¹⁰ - 900x⁵ + 1000
729x¹⁵ - 810x¹⁰ + 810x¹⁰ + 900x⁵ - 900x⁵ + 1000
729x¹⁵ + 1000

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$\sf\ .04=\frac{4}{100}\\\\x=\frac{4}{100}\times350\\\\x=\frac{4\times350}{100}\\\\x=\frac{1400}{100}={\boxed{14}$

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