Finding (p+q)(x) and (p/q)(x) with p(x)=x²-5x and q(x)=x-5

[math4life]

Homework Statement

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)

Homework Equations

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.

 

[benk99nenm312]

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

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.

 

[Mark44]

Homework Statement

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)

Homework Equations

The Attempt at a Solution

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

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.

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

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.

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



Thanks.