Question

if the polynomial x^3 - 3x^2 + kx +42 is divisible by x+3 then find the value of k

Answer 1

p(x)= x^3-3x^2+kx+ 42=0
p(-3)= (-3^3)-(-3*3^2)+k*(-3)+42=0 { x+3 is the factor of px then x=(-3) is the zero of polynomial px}
p(-3)= -27+81-3k+42=0
p(-3)= -27+123-3k=0
p(-3)= 96-3k=0
p(-3)= -3k= -96
p(-3)= k= -96/-3
p(-3)= k= 32

Therefore the value of k= 32
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