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Polynomials

Short Answer Type

91. Find the remainder obtained when x⁴ + 3x³ - 2x² + x + 1 is divided by x - 1.

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92. Check whether the polynomial q(t) = 4t³ + 4t² - t -1 is a multiple of 2t + 1.

Solution not provided.

Ans. Yes

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93. If the polynomial p(x) = x⁴- 2x³ + 3x² - ax + 8 is divided by (x - 2), it leaves a remainder 10. Find the value of a.

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94. The polynomials x³ + 2x² - 5ax - 8 and x³ + ax² - 12x - 6 when divided by (x - 2), and (x - 3) leave remainder p and q respectively. If q - p =10. find the value of a.

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95. The polynomials kx³ + 3x² - 8 and 3x³ - 5x + 8 are divided by x + 2. If the remainder in each case in the same, find the value of k.

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96. If f(x) = x⁴- 2x³ + 3x² - ax + b is divided by (x - 1) and (x + 1), it leaves the remainder 5 and 19 respectively. Find ‘a’ and ‘b’.

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97. Find the remainders when 3x³- 4x² + 7x - 5 is divided by (x - 3) and (x + 3).

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98. If p(x) =x³ - ax² + bx + 3 leaves a rer.idinder -19 when divided by (x + 2) and a remainder 17 when divided by (x - 2), prove that a + b = 6.

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99. If remainder is same when polynomial p(x) = x³ + 8x² + 17x + ax is divided by (x + 2) and (x + 1), find the value of a.

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100. The polynomials ax³ + 3x² - 13 and 2x³ - 5x + a are divided by x - 2. The remainder in each case is the same. Find the value of a.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

92. Check whether the polynomial q(t) = 4t3 + 4t2 - t -1 is a multiple of 2t + 1.

92. Check whether the polynomial q(t) = 4t³ + 4t² - t -1 is a multiple of 2t + 1.