Find the polynomial of least degree which should be subtracted from the polynomial x4 + 2x3 – 4x2 + 6x – 3 so that it is exactly divisible by x2 – x + 1.

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Answer is x-1
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x-1
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Shivam Dubey | Home Tutor – Maths & Psychology with +7 years of experience

For example, when we divide 17 by 5, the remainder is 2. If we subtract 2 from 17, we get 15, which is exactly divisible by 5. Similarly, in polynomial division, we subtract the remainder from the given polynomial to make it exactly divisible by the divisor.
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For example, when we divide 17 by 5, the remainder is 2. If we subtract 2 from 17, we get 15, which is exactly divisible by 5. Similarly, in polynomial division, we subtract the remainder from the given polynomial to make it exactly divisible by the divisor. read less
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Remainder = x-1
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5x-1
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X-1
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As we know Dividend = Quotient x Divisor + Remainder So, we can write Dividend - Remainder = Quotient x Divisor So we observe that if we subtract the remainder from the dividend, the resultant will be divisible by Divisor. Using this concept, if we divide x2-x+1 with x4+2x3-4x2+6x-3 , then the remainder...
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As we know Dividend = Quotient x Divisor + Remainder So, we can write Dividend - Remainder = Quotient x Divisor So we observe that if we subtract the remainder from the dividend, the resultant will be divisible by Divisor. Using this concept, if we divide x2-x+1 with x4+2x3-4x2+6x-3 , then the remainder obtained is the polynomial which should be subtracted from the given polynomial. so if we divide x4 + 2x3 – 4x2 + 6x – 3 with x2-x+1, we get x-1 as remainder. Hence, x-1 should be subtracted from the polynomial. read less
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BE (Electronics And Communications) Tutor

firstly we divide x2-x+1 with x4+2x3-4x2+6x-3 , then the remainder is the polynomial ( x-1 )which should be subtracted the given polynomial. So, the answer is the (x-1).
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