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Polynomials

Short Answer Type

81. Find the remainder when x³ + 3x² + 3x + 1 is divided by
5 + 2x

145 Views

82. Find the remainder when x³ - ax² + 6x - a is divided by x — a.

288 Views

83. Check whether 7 + 3x is a factor of 3x³ + 7x.

283 Views

84. The polynomial p(x) = kx³ + 9x² + 4x - 8 when divided by x + 3 leaves a remainder - 20. Find the value of k.

427 Views

85. The polynomial p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7. When divided by (x + 1) leaves the remainder 19. Find the value of a. Also find the remainder, when p(x) is divided by x + 2.

p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7

By remainder theorem.

p(- 1) = 19 | x + 1 = 0 $rightwards double arrow$ x = -1

$rightwards double arrow$ (- 1)⁴ - 2 (- 1)³ + 3 (- 1)²- a(- 1) + 3a - 7 = 19
$rightwards double arrow space$ 4a = 20

$rightwards double arrow space space space space space space space space space space space space space space straight a space space equals space 20 over 4 equals space 5$

Also, the remainder when p(x) is divided by x + 2

= p(-2)
= (-2)⁴ - 2 (-2)³ + 3(-2)²- a(-2) + 3a - 7
= 16 + 16 + 12 + 2a + 3a - 7
= 5a + 37
= 5(5) + 37
= 25 + 37
= 62

1944 Views

86. The polynomials ax³ - 3x² + 4 and 2x³ - 5x + a when divided by (x - 2) leave the remainders p and q respectively. If p - 2q = 4, find the value of a.

2188 Views

87. The polynomials ax³ + 3x² - 3 and 2x³ - 5x + a when divided by x - 4 leaves the remainders p and q respectively. Find the value of a, if 2p = q.

876 Views

88. Divide p(x) by g(x) using long division method, where p(x) = x + 3x² - 1 and g(x) = 1 + x.

122 Views

89. Using long division method divide the polynomial 3x⁴ - 4x³ - 3x - 1 by x - 1.

177 Views

90. Using long division method, find the remainder obtained on dividing p(x) = x² + 1 by x + 1.

125 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

85. The polynomial p(x) = x4 - 2x3 + 3x2 - ax + 3a - 7. When divided by (x + 1) leaves the remainder 19. Find the value of a. Also find the remainder, when p(x) is divided by x + 2.

85. The polynomial p(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7. When divided by (x + 1) leaves the remainder 19. Find the value of a. Also find the remainder, when p(x) is divided by x + 2.