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Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2?
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Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x -...
Proving Divisibility without Division
To prove that 2x4 - 6x3 + 3x2 + 3x - 2 is exactly divisible by x2 - 3x + 2 without using division, we can follow these steps:
- Step 1: Check the roots of the divisor
- Step 2: Use Remainder Theorem
- Step 3: Substitute the roots of the divisor
Step 1: Check the roots of the divisor
The roots of x2 - 3x + 2 are x = 1 and x = 2. Therefore, the divisor can be factored as (x - 1)(x - 2).
Step 2: Use Remainder Theorem
According to the Remainder Theorem, if we substitute the roots of the divisor into the polynomial 2x4 - 6x3 + 3x2 + 3x - 2, the remainder will be zero if the polynomial is divisible by the divisor.
Step 3: Substitute the roots of the divisor
Substitute x = 1 and x = 2 into the polynomial:
For x = 1: 2(1)4 - 6(1)3 + 3(1)2 + 3(1) - 2 = 2 - 6 + 3 + 3 - 2 = 0
For x = 2: 2(2)4 - 6(2)3 + 3(2)2 + 3(2) - 2 = 32 - 48 + 12 + 6 - 2 = 0
Since the remainder is zero for both roots, the polynomial 2x4 - 6x3 + 3x2 + 3x - 2 is exactly divisible by x2 - 3x + 2.
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Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2?
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Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2?.
Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Without division prove that 2x power 4 - 6x power 3 + 3x square + 3x - 2 is exactly divisible by X square - 3x +2?.
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