# I need a little help!

#### lindsayvickroy

##### New member
The question I need help with is:

P(X) is a Polynomial of degree 4 with real coefficents and roots 5, -4, and 3+i. Find P(X).

I've gotten to (x-5)(x+4)(x-3-i)(x-3+i) but I need a little help from there.

#### pka

##### Elite Member
Well, [x-(3+i)][x-(3-i)]=x<SUP>2</SUP>-6x+10 and (x-5)(x+4)= x<SUP>2</SUP>-x-20.
Now you finish it.

#### lindsayvickroy

##### New member
I don't know why I'm having such a hard time with this problem! If you could walk me through the rest of it I would appreciate it.

Staff member

#### tkhunny

##### Moderator
Staff member
(x<SUP>2</SUP>-6x+10)*(x<SUP>2</SUP>-x-20)
Remember how to multiply large numbers? Just match each digit from one with each digit from the other. It is the same, here. 3 in one and 3 in the other, you should have nine multiplications to track down.

Here's a way to split it up into three sets of three.

(x<SUP>2</SUP>-6x+10)*(x<SUP>2</SUP>-x-20)

x<SUP>2</SUP>*(x<SUP>2</SUP>-x-20) - 6*(x<SUP>2</SUP>-x-20) + 10*(x<SUP>2</SUP>-x-20)

Keep going...