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____ [38]
3 years ago
14

What is the factored form of 125x6 – 8?

Mathematics
2 answers:
valina [46]3 years ago
8 0

Answer:

(5x^2-2)(25x^4+10x^2+4)

Step-by-step explanation:

Given expression,

125x^6-8

=(5)^3 (x^2)^3 -2^3    \because (ab)^m=a^mb^m\text{ and }a^{mn}=(a^m)^n

=(5x^2)^3+(-2)^3

By using a³ + b³ = (a-b) (a² -ab + b² )

=(5x^2+(-2)) ((5x^2)^2 - (5x^2\times -2) + (-2)^2)

=(5x^2-2)(25x^4+10x^2+4)

Which is the required factor form,

Third option is correct.

Vaselesa [24]3 years ago
5 0
Hello,

Answer C

125x^6-8=(5x²)^3-2^3=(5x²-3)((5x²)²+2*5*x²+4)

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F(x) = x^2. What is g(x)
Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

  • If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
  • If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
  • If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  
  • If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  
  • If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k  

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

   graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

4 0
3 years ago
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