if the polynomial p(x)=kx^3+15x^2+9x-76 is divisible by (x+4),find the value of k.
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( X + 4 ) is a factor of the given polynomial kx³ + 15x² + 9x - 76.
( X + 4) = 0
X = -4
P ( X ) = KX³ + 15X² + 9X - 76
P (-4) = K × (-4)³ + 15 × (-4)² + 9 × -4 - 76
=> K × -64 + 15 × 16 - 36 - 76 = 0
=> -64k + 240 - 112 = 0
=> -64k + 128 = 0
=> -64k = -128
=> k = 128/64
=> K = 2.
( X + 4) = 0
X = -4
P ( X ) = KX³ + 15X² + 9X - 76
P (-4) = K × (-4)³ + 15 × (-4)² + 9 × -4 - 76
=> K × -64 + 15 × 16 - 36 - 76 = 0
=> -64k + 240 - 112 = 0
=> -64k + 128 = 0
=> -64k = -128
=> k = 128/64
=> K = 2.
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