$\displaystyle 8x^3 + 10x^2 - px -5$ is divisible by $\displaystyle 2x + 1$ . There is no remainder. Find the value of P.
What do I have to do to find p?
Hi Devi09,
There's a couple of things you can do here. Do you know synthetic division?
You could use $\displaystyle \frac{-1}{2}$ as your divisor and find P that way.
Perhaps an easier method would be to act like $\displaystyle 2x + 1$ is a factor of $\displaystyle f(x)=8x^3+10x^2-px-5$ in which case $\displaystyle x = -\frac{1}{2}$ is a root. (Factor Theorem)
Now, set $\displaystyle f(x)=0$ and find $\displaystyle f(-\frac{1}{2})$. (Remainder Theorem.) $\displaystyle f(x)=0$ means when $\displaystyle -\frac{1}{2}$ is substituted for x, the remainder is 0.
Once you've substituted $\displaystyle -\frac{1}{2}$ for x, you'll can solve for p.
$\displaystyle 8(-\frac{1}{2})^3+10(-\frac{1}{2})^2-p(-\frac{1}{2})-5=0$
I got another question. Lets say $\displaystyle x^6 + x^4 - 2x^2 + k$ is divided by $\displaystyle 1 + x^2$ and the remainder is 5 and you need to find k
So $\displaystyle f(sqrt(-1))$
$\displaystyle (sqrt-1)^6 + (sqrt-1)^4 - 2(sqrt-1)^2 + k = 5$
but -1 can't be square rooted so what would you do?