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30 points 1 question PLEASE HELP ME OUT I REALLY NEED IT

Given p(x)=3x^5+2x^2−5, Alonso wants to find out whether 3x+5 is a factor. Which value of x should he evaluate for p(x) to determine the answer?
I got -5/3 which is correct I just need value of the function at the x-value you selected?

Respuesta :

Answer:

p(-5/3) ≠  0 So, (3 x +5) is NOT A FACTOR of p(x)

Step-by-step explanation:

Here, the given function is [tex]p(x)=3x^5+2x^2 - 5[/tex]

Now, the given root of the function is ( 3x +5)

Now, if ( 3 x +  5) = 0,

we get x = - 5/3

So, the zero of the given polynomial is x = -5/3

Then,  x = -5/3, p(x)  =0 ⇒   ( 3 x + 5) is a FACTOR of p(x)

Now, let us find the value of function at x = -5/3

Substitute x = -5/3 in the given function p(x), we get:

[tex]p(x)=3x^5+2x^2 - 5  \implies p(\frac{-5}{3})  = 3(\frac{-5}{3})^5 + 2(\frac{-5}{3})^2 - 5\\= 3(\frac{-3,125}{243}) + 2(\frac{25}{9})  - 5\\= (\frac{-3,125}{81}) + (\frac{50}{9})  - 5\\= -38.580 + 5.56  - 5  =  -38.02\\\implies p(\frac{-5}{3})  = -38.02[/tex]

Now, as p(-5/3) ≠  0 So, (3x +5) is NOT A FACTOR of p(x)

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