Prove that :- 1 + i^2 + i^4 + i^6 = 0

Find value of k for which (x - 1) is a factor of (2x³ - 9x² + x + k)

Find remainder and quotient of 6x³ + 13x² + 3 divide by 3x + 2

By actual division find the quotient and remainder when x⁴ + 1 is divided by x-1

Show that 2x - 3 is a factor of 2x³ - 9x² + x + 12

Find remainder when x³ - 2x² - 8x - 1 is divided by x +1

Divide 3x⁵ - 4x⁴ + 3x³ + 2x by x² - 3 using synthetic method

Find remainder p(x) = 3x⁴ - 6x² - 8x - 2, g(x) = x - 2

Find value of a for which (x + 1) is a factor of (ax³ + x² - 2x + 4a - 9)

Solve 3x² + 11x + 10 = 0

If A + B = 45, Prove that (1 + tanA) (1 + tanB) = 2

Show that p - 1 is a factor of p^10 - 1 and also p^11 - 1

If (x - a) is a factor of (x³ - ax² + 2x + a - 1) then find the value of a

If points A(4, 3) and B(x, 5) are on circle with centre O(2, 3), find the value x

If p(x) = x³ - x + 1 and g(x) = 2 - 3x. check whether p(x) is a multiple of g(x)

Find Remainder p(x) = 2x² - 7x² + 9x - 13, g(x) = x - 3

Find value of a for which (x - 4) is a factor of (2x³ - 3x² - 18x + a)

If A + B = 45 Prove that (cotA - 1)(cotB - 1) = 2

Find values of x for which distance between points P(4, -5) and Q(12, x) is 10 units

If Polynomials 2x³+ ax² +3x -5 and x³ + x² - 2x + a leave same remainder when divided by x-2, Find a

If p(x) = x³ - 5x² + 4x - 3 and g(x) = x - 2, show that p(x) is not a multiple of factor g(x)

Polynomials (2x³ + x² - ax +2) and (2x³-3x²-3x+a) when divided by (x-2) leave same remainder. Find a

Find quotient and remainder of 2x³ - 9x² + x +15 dividing by 2x - 3

If p(x) = 2x³ - 11x² - 4x + 5 and g(x) = 2x + 1 show that g(x) is not a factor of p(x)

Find quotient and remainder p(x) = x³ - 6x² + 9x + 3 , g(x) = x - 1