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zzz [600]
2 years ago
10

Which of the following is a factor of f(x) = 5x3 + 24x2 − 75x + 14?

Mathematics
2 answers:
morpeh [17]2 years ago
4 0

Answer:

<em>(x-2)</em><em> is a factor of the function.</em>

Step-by-step explanation:

Given function is,

f(x) = 5x^3+24x^2-75x+14

As when we equate any factor of a polynomial to zero, the value of x we get is the zero of the polynomial.

So equating all the options to 0, we get

  1. x+\dfrac{1}{2}=0\ \ \ \ \Rightarrow x=-\dfrac{1}{2}
  2. x-\dfrac{1}{2}=0\ \ \ \ \Rightarrow x=\dfrac{1}{2}
  3. x+2=0\ \ \ \ \Rightarrow x=-2
  4. x-2=0\ \ \ \ \Rightarrow x=2

If x is a zero of a polynomial, then after putting the value of x in the polynomial, it becomes 0.

So,

  1. f(-\dfrac{1}{2}) = 5(-\dfrac{1}{2}) ^3+24(-\dfrac{1}{2}) ^2-75(-\dfrac{1}{2}) +14=\dfrac{455}{8}\neq 0
  2. f(\dfrac{1}{2}) = 5(\dfrac{1}{2}) ^3+24(\dfrac{1}{2}) ^2-75(\dfrac{1}{2}) +14=-\dfrac{135}{8}\neq 0
  3. f(-2) = 5(-2)^3+24(-2)^2-75(-2)+14=220\neq 0
  4. f(2) = 5(2)^3+24(2)^2-75(2)+14=0

So, (x-2) is a factor of the function.

Semmy [17]2 years ago
3 0
Thank you for posting your question here at brainly. Feel free to ask more questions.  

The best and most correct answer among the choices provided by the question is <span>(x − 2)</span>.<span>       
    </span><span>
Hope my answer would be a great help for you.</span>
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