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)