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x= -4

x+4=0

Dividing equation by x+4

x³-x²-14x+24/x+4

After diving we will get

x²-5x+6 = 0

Taking out its factors

x²-2x-3x+6 = 0

x(x-2)-3(x-2) = 0

(x-2) (x-3) = 0

x-2=0, x-3=0

x=2, x=3

therefore, Zeros are -4,2,3

I hope this will help you!

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If -4 is a zero of the polynomial P(x) then (x+4) is a factor of P(x). So

(x+4) (x² + a x + 6) = P(x) = x³ - x² - 14 x + 24

co-efficient of x² is 1 as coefficient of x³ = 1 in P(x),

constant term is 24 in P(x), so 24/4 = 6 is the constant term in the second factor.

So co-efficient of x² = 4 + a = -1 So a = -5

co-efficient of x = 4a + 6 = -20 + 6 = -14. So it verifies.

(x+4) (x² + a x + 6) = P(x) = x³ - x² - 14 x + 24

co-efficient of x² is 1 as coefficient of x³ = 1 in P(x),

constant term is 24 in P(x), so 24/4 = 6 is the constant term in the second factor.

So co-efficient of x² = 4 + a = -1 So a = -5

co-efficient of x = 4a + 6 = -20 + 6 = -14. So it verifies.