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Which of the following is one of the factors of x4+4?
- a)x2+2
- b)(x² + 2 + 2x)(x² + 2 - 2x)
- c)x2−2
- d)x2+2x−2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Which of the following is one of the factors ofx4+4?a)x2+2b)(x² +...
x4+4
adding and subtracting 4x2
x4+4+4x2−4x2
(x2)2+22+2∗2∗x2−(2x)2
(x2+2)2−(2x)2(a+b)2=a2+b2+2ab
(x2+2−2x)(x2+2+2x)(a2−b2)=(a+b)(a−b)
Most Upvoted Answer
Which of the following is one of the factors ofx4+4?a)x2+2b)(x² +...
The given expression is x^4 + 4.
To find the factors, we can use the factoring formula a^2 - b^2 = (a+b)(a-b).
Using this formula, we can rewrite the expression as (x^2)^2 + 2^2, which is in the form a^2 + b^2.
So, the factors of the expression are (x^2 + 2)(x^2 - 2).
None of the given options, a) x^2 + 2 or b) (x is a factor of the given expression.
To find the factors, we can use the factoring formula a^2 - b^2 = (a+b)(a-b).
Using this formula, we can rewrite the expression as (x^2)^2 + 2^2, which is in the form a^2 + b^2.
So, the factors of the expression are (x^2 + 2)(x^2 - 2).
None of the given options, a) x^2 + 2 or b) (x is a factor of the given expression.
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