CBSE 10 - Maths Solve it
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CBSE 10 - Maths answer this question
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CBSE 10 - Maths Asked by harshkumar128198k | 29 Mar, 2022, 04:19: PM ANSWERED BY EXPERT We know that, f(x) = g(x) x q(x) + r(x) f(x) - r(x) = g(x) x q(x) f(x) + {- r(x)} = g(x) x q(x) Clearly , Right hand side is divisible by g(x). Therefore, Left hand side is also divisible by g(x).Thus, if we add - r(x) to f(x), then the resulting polynomial is divisible by g(x). Let us now find the remainder when f(x) is divided by g(x). Hence, we should add - r(x) = x - 2 to f(x) so that the resulting polynomial is divisible by g(x). Page 2We know that Dividend = Quotient x Divisor + Remainder. Dividend - Remainder = Quotient x Divisor. Clearly, Right hand side of the above result is divisible by the divisor. Therefore, left hand side is also divisible by the divisor. Thus, if we subtract remainder from the dividend, then it will be exactly divisible by the divisor. Dividing x4 + 2x3 − 13x2 − 12x + 21 by x2 − 4x + 3 Therefore, quotient = x2 + 6x + 8 and remainder = (2x - 3). Thus, if we subtract the remainder 2x - 3 from x4 + 2x3 − 13x2 − 12x + 21 it will be divisible by x2 − 4x + 3. |