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2 years ago

Factor the following expression x^4 - 11x^2 + 10 ty

Mathematics

1 answer:

Verdich [7]2 years ago

7 0

Answer:

( x - 1 ) × ( x + 1 ) × ( x^2 - 10)

Step-by-step explanation:

x^4 - 11x^2 + 10

x^4 - x^2 - 10x^2 + 10

x^2 × ( x^2 - 1 ) - 10( x^2 - 1 )

( x^2 - 1 ) × ( x^2 - 10 )

( x - 1 ) × ( x + 1 ) × ( x^2 - 10)

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Answer:

OPTION C

Step-by-step explanation:

We have the following rules:

$\sqrt[a]{x} = x^{\frac{1}{a}$ and

$x^a . x^b = x^{a + b}$

OPTION A: $x \sqrt[7]{x}$

= $x . x^{\frac{1}{7}$

= $x^{1 + \frac{1}{7}$

$= x^{\frac{8}{7}$ $\ne x^{\frac{9}{7}$

So, it can be eliminated.

OPTION B: $\bigg ( \frac{1}{\sqrt[7]{x}} \bigg )^9$

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So, this option is also eliminated.

OPTION C: $x . \sqrt[7]{x}$

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= $x^{1 + \frac{1}{7}}$

= $x^{\frac{9}{7}}$

So, OPTION C is the answer.

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