Question

Use the factor theorm to determine the value of k when x+2 is an factor of (x+1)^7+(2x+k)^3

Answer 1

x +2 = 0

x = -2

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p(x) = (x+1)⁷ + (2x+k)³ = 0

p(-2) = (-2+1)⁷ + (-4+k)³ = 0

$\implies$ (-1)⁷ + (-4+k)³ = 0

$\implies$ -1 + (-4+k)³ = 0

$\implies$ (-4+k)³ = 1

$\implies$ -4+k = ³$\sqrt{1}$

$\implies$ -4+k = 1

$\implies$ k = 1+4

$\implies$ k = 5 ..ans....