Thank you for the opportunity to help you with your question!

I WII USE AN EXAMPLE ON HOW TO SOLVE SYNTHETIC DIVISION WITH A RADICAL FACTOR: determine whether x
– 4 is a factor of:

–2x^{5}
+ 6x^{4} + 10x^{3} – 6x^{2}
– 9x + 4

For x
– 4 to be a factor,
you must have x
= 4 as a zero. Using
this information, I'll do the synthetic division with x
= 4 as the test zero
on the left:

Since the remainder is
zero, then x
= 4 is indeed a zero
of –2x^{5}
+ 6x^{4} + 10x^{3} – 6x^{2}
– 9x + 4,
so:

Yes, x
– 4 is a factor of –2x^{5}
+ 6x^{4} + 10x^{3} – 6x^{2}
– 9x + 4

Please let me know if you need any clarification. I'm always happy to answer your questions.

may you please show me an example that the factor has a radical please i don't understand how to add and multiply radical but i understand the procedure of synthetic division