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Class 10 > Find the polynomial of least degree which should be...
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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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Remainder = 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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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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