Is (x+4) a factor of 7x^4 +23x^3-15x^2+21x+4? There are various ways to solve the problem.

There are various ways to solve the problem. Answer yes or no:______

yes of course,

This question relies on knowledge about factor theorem and/or remainder theorem.

Which states:

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. That is:
p(x) = (x – a)q(x)

So if you substitute x= - 4 into the above equation

7(-4)^4 +23(-4)^3 -15(-4)^2 + 21(-4) + 4 = .....

There are a few way to approach this question, you can use the methods as follows
1) polynomial long division

http://www.sosmath.com/algebra/factor/fa…

2) factor theorem or remainder theorem

http://www.purplemath.com/modules/factrt…

If x+4 is a factor, then x=-4 is a zero.

Using synthetic division is one way to check:

-4) 7. 23. -15. 21. 4
_________________
......7...-5.....5.....1...(0

Since the remainder is zero, -4 is a zero, and x+4 is a factor.

Hoping this helps.