Verified Answer :

Answer:

Option A is correct.

\(x^2+3x-40\)

Step-by-step explanation:

Given the real zeroes at x = -8 and x = 5.

Factor theorem states that (x-r) is a factor of the polynomial function f(x) if and only if r is a root of the function f(x).

Since, we know that the root of the function i.e f(x) are -8 and 5 then the function has the following factor:

(x+8) = 0 and (x-5) =0

Zero product property states that if ab = 0 if and only if a =0 and b =0.

By zero product property,

(x+8)(x-5) = 0

Now, distribute each terms of the first polynomial to every term of the second polynomial we get;

\(x(x-5) +8(x-5)\)

Now, when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.

\(x^2-5x+8x-40\)

Combine like terms;

\(x^2+3x-40\)

therefore, the function \(x^2+3x-40\) has real zeros at x = -8 and x =5

Answer:

g(x) = \(x^{2} + 3x-40\) for real zero x= -8, x =5.

Step-by-step explanation:

Given : real zeros x =-8 , x =5 .

To find : Function.

Solution : We have given that:

Factor theorem states that (x-r) is a factor of the polynomial function f(x) if and only if r is a root of the function f(x).

Since, we know that the root of the function i.e f(x) are -8 and 5 then the function has the following factor:

(x+8) = 0 and (x-5) =0

Zero product property states that if ab = 0 if and only if a =0 and b =0.

By zero product property,

(x+8)(x-5) = 0

Now, distribute each terms of the first polynomial to every term of the second polynomial we get;

x (x-5 ) +8(x-5)

\(x^{2}-5x +8x-40\).

\(x^{2} + 3x-40\).

Therefore, g(x) = \(x^{2} + 3x-40\) for real zero x= -8, x =5.

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