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Factorize :- x² + 20x - 69

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Factorize :- x² + 18x + 32

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

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

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If x³ + ax² + bx + 6 has x-2 as a factor and leaves a remainder 3 when divided by x-3. find a and b

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Prove that 2x⁴ - 5x³ + 2x² - x + 2 is divisible by x² - 3x + 2

Find value of √(-36) * √(16)

If (x + 2a) is a factor of x⁵ - 4a²x³ + 2x + 2a + 3, Find a

Show that x - 1 is a factor of 2x⁴ + 9x³ + 6x² -11x - 6

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Find value of a for which polynomial (x⁴ - x³ - 11x² - x + a) is divisible by (x + 3)

Factorize :- x² + 20x - 69

Factorize :- x² + 11x + 30

Express (1 - 2i)^-3 in standard form a + ib

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Integrate : ∫ x log(x + 1) dx

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Factorize : 2x² - 7x - 15

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Prove that tan⁻¹(cosx / 1 - sinx) = π/4 + x/2, x ∈ (-π/2 , π/2)

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