Divide. (4x^4 - 4x^2 - x-3) = (2x^2 – 3)
1 answer:
Answer:
Step-by-step explanation:
<u>Step 1:</u>
- Simplify:
<em>Checking for a perfect cube:</em>
- 4x⁴ - 4x² - x - 3 is not a perfect cube.
<em>Trying to factor by pulling out:</em>
- Factoring: 4x⁴ - 4x² - x - 3
- Thoughtfully split the expression at hand into groups, each group having two terms:
- Group 1: - x - 3
- Group 2: 4x⁴ - 4x³
- Pull out from each group separately:
- Group 1: (x + 3) • (-1)
- Group 2: (x² - 1) • (4x²)
- Bad news!! Factoring by pulling out fails:
- The groups have no common factor and can not be added up to form a multiplication
<em>Final result:</em>
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The irrational numbers are: √8, √10 and √15
Step-by-step explanation:
A rational number is a number that can be written in the form p/q where p&q are integers and q≠0.
"All the numbers whose square root is not a whole number and has an infinite number of digits after decimal, are irrational numbers"
So in the given options
Which can be written in the required form so √4 is a rational number
√8 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number
√10 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number
√15 has an infinite expansion hence it cannot be written in the p/q form, so it is an irrational number
Which can be written in the required form so √36 is a rational number
Hence,
The irrational numbers are: √8, √10 and √15
Keywords: Rational numbers, Irrational numbers
Learn more about rational numbers at:
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