Question

How do I solve the following problem?

"p(x)=3(x^2 +10x+5)-5(x-k)
In the polynomial p(x) defined above, k is a constant. If p(x) is divisible by x, what is the value of k?"
How would I go about solving this problem

Answer 1

Explanation:

You need to make the constant =0 Because in order for x to be divisible it needs to go in even so if you had 0/x that would solve your problem

EX. x²-x can be divided evenly by x with out a remainder

but x²-x+5 when dividing you get a remainder of 5/x

So simplify equation first

p(x)=3x²+30x+15-5x+5k

=3x²+25x+15+5k

take the constant and set it =0

15+5k=0

k= -3

So when k is -3 your constant is 0

no x can be divisible by the equation.