Answer:
Option A is correct.
[tex]x^2+3x-40[/tex]
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;
[tex]x(x-5) +8(x-5)[/tex]
Now, when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.
[tex]x^2-5x+8x-40[/tex]
Combine like terms;
[tex]x^2+3x-40[/tex]
therefore, the function [tex]x^2+3x-40[/tex] has real zeros at x = -8 and x =5
Answer:
g(x) = [tex]x^{2} + 3x-40[/tex] 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)
[tex]x^{2}-5x +8x-40[/tex].
[tex]x^{2} + 3x-40[/tex].
Therefore, g(x) = [tex]x^{2} + 3x-40[/tex] for real zero x= -8, x =5.
