Question

Factorize: 1.x⁴+ 7x² +16
2.x²+ 1/x²-2-3x +3/x​

Answer 1

Answer:

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Step-by-step explanation:

How do I simplify (x⁴ - 27x)/(x² - 9) ÷ (x² + 3x + 9) / (x + 3)?

Since dividing by an expression is equivalent to multiplying by its reciprocal, then

(x⁴ - 27x) / (x² - 9) ÷ (x² + 3x + 9) / (x + 3) = (x⁴ - 27x) (x +3) / (x² - 9) (x² + 3x + 9)

Note the factor (x⁴ - 27x) in the numerator has a common factor of x and what remains is a difference of cubes so that

(x⁴ - 27x) = x (x-3) (x² + 3x + 9).

Also, the factor (x² - 9) in the denominator is a difference of squares so that

(x² - 9) = (x – 3) (x + 3).

Now, provided x does not equal 3 or -3, you can divide out the factors (x - 3), (x + 3) and (x² + 3x + 9) leaving x for the simplified answer.