polynomial problem

[Andrew131]

The polynomial 4x^3 + ax + 2, where a is a constant, is denoted by p(x). It is given that 2x + 1 is a factor of p(x).
(i) Find the value of a.

(ii) When a has this value

(a) factorise p(x)

(b) solve inequality p(x)> 0, justifying your answer

Answer:

I found the value of a equal to 3 by using the factor theorem.

Then I factorised p(x) by dividing p(x) by 2x+1 and got quotient 2x^2-x+2.

so p(x) = (2x+1) (2x^2-x+2)

I was not able to do number b . I don't really know what it is trying to say.

 

[Steven G]

When is (2x+1) positive, when is it negative? When is (2x^2 - x+ 2) positive/negative.

If Y*Z>0, then what can the signs of X and Y be???