Question

Check whether 7 + 3x is a factor of 3x³ + 7x.

Answer 1

p(x) = 3x³ + 7x 

Let g(x) = 7 + 3x = 0. then 

If 7 + 3x = 0, then 3x = -7 

x = - \(\frac{7}{3}\)

If p(x) is divided by p(z), remainder r(x) – 0, then g(x) is a factor. 

p(x) = 3x³ + 7x

Here, r(x) = - \(\frac{500}{9}\). 

This is not equal to Zero. 

Hence 7 + 3x is not a factor of p(x).