# (p+q)(x) & (p/q)(x)

1. Jun 28, 2009

### math4life

1. The problem statement, all variables and given/known data

Given p(x)=x2-5x and q(x)=x-5:

1) Find (p+q)(x) and (p/q)(x)

2) Find (p o q)(x) and (p o q)(-3) (I did this correct I think)

2. Relevant equations

3. The attempt at a solution

1) I am thinking this is just (x2-5x+x-5) and (x2-5x)/(x-5). Is this correct?

2) I did the work below on these. Please verify the answers.

(P o q)(x)= (x-5)2-5[(x)(-5)]=x2-10x+25-5x+25
x2-15x+50=(x-5)(x-10)= 5, 10

(P o q)(-3)= (-3-5)2-[5(-3-5)]=64+15+25=104

Thanks.

2. Jun 28, 2009

### benk99nenm312

When you have (P of (Q (x)), you should not get a numerical answer. (x-5)(x-10) is as simple as it gets. You tried to take it one step to far, aand in doing so, implied (x-5)(x-10) was = to 0. x2-15x+50 would suffice. You knew the answer, you just tried to go to far.

All the rest looks okay to me.

Thumbs up mate.

3. Jun 29, 2009

### Staff: Mentor

Yes, they are correct, but should be simplified. For the first one, there are two like terms that should be combined. For the second, the numerator and denominator have common factors.
This part is incorrect - (x-5)(x-10)= 5, 10 As was already pointed out, (p o q)(x) can be written as either (x - 5)(x - 10) or x2 - 10x + 50. To get the two numbers 5 and 10, you have assumed that x2 - 10x + 50 = 0, and there is no reason to do so.

In any case, (x - 5)(x - 10) is not equal to 5 nor is it equal to 10.