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Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.
  Yes. When the function f(x) = x3 − 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 − 75x + 250.
 
No. When the function f(x) = x3 − 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is not a factor of f(x) = x3 − 75x + 250.
 
Yes. When the function f(x) = x3 − 75x + 250 is divided by x + 10, the remainder is not zero. Therefore, x + 10 is a factor of f(x) = x3 − 75x + 250.
 
No. When the function f(x) = x3 − 75x + 250 is divided by x + 10, the remainder is not zero. Therefore, x + 10 is not a factor of f(x) = x3 − 75x + 250.

Respuesta :

Jieep
Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250. 

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a). 
In this case, 
f(x)=x^3-75x+250 
(x+a)=(x+10) 
Therefore, the remainder f(-a)=f(-10) 

=x^3-75x+250 
=(-10)^3-(75*-10)+250 
=-1000+750+250 
=1000-1000 
=0. 
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.
zame

Answer:

A)  Yes. When the function f(x) = x3 − 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 − 75x + 250.

Step-by-step explanation:

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