1. ## polynomial division

Hi everybody, this is my first post, I am coming here in search for some fine help. Thanks an advance to anyone who can help me with these problems

I have some I need check and some I am not sure how to approach.

The first one is division of polynomials.

(-15x3 -10x2+13x-5) Divded By (3x+5)

the smaller ones are cubed and squared, I can't figure out how to make the squared on here yet sorry.

The next I need checked is...

-3/x+5 - 4/x-5 = 2/ x2-25

I got x= -1 as my answer.

Next is: A baker can decorate the day's cookie supply four times as fast as his new assistant. If they decorate all the cookies working together in 32 minutes, how long would it take each one working individually to decorate all the cookies?

The time, t required to empty a tank varies inversely as the rate r of pumping. if a pump can empty a tank in 45 minutes at the rate of 600kL/min, how long will it take the pump to empty the same tank at the rate of 100kL/min?

the last two are a little confusing to me. thanks

2. Hello,

You generally have this equality :

$\underbrace{P(X)}_{\text{polynom \ of \ nth \ degree}} = \underbrace{Q(X)}_{\text{1 \ degree}} \underbrace{R(X)}_{\text{n-1 \ degree}}$

But this is only if you know that 3x+5 indeed divides the polynom.
If you don't know, work by steps :

$(-15x^3 -10x^2+13x-5)$

Study the term of highest degree : $-15x^3$

This is 3x (-5x²)

So write it :

$-15x^3 -10x^2+13x-5 = -5x^2(3x+5) - Q(X)$

-5x²*5=-25x², so you have to add this term since you substracted it

$-15x^3 -10x^2+13x-5 = -5x^2(3x+5) + 25x^2 \underbrace{-10x^2+13x-5}_{\text{the \ remaining \ of \ the \ very \ first \ polynom}}$

$= -5x^2(3x+5)+15x^2+13x-5$

Work the same way for 15x² = (3x)*5x

$= -5x^2(3x+5) + \underbrace{5x(3x+5)}_{\text{new \ term}} + R(X)$

5x*5 = 25x

-> $= -5x^2(3x+5) + 5x(3x+5) - 25x+13x-5$

--> $=(3x+5)(-5x^2+5x) - 12x -5$

Again, -12x=(3x)*(-4)

$= (3x+5)(-5x^2+5x) - 4(3x+5) - S(X)$

-4*5=-20

$= (3x+5)(-5x^2+5x-4)+20-5=(3x+5)(-5x^2+5x-4)+15$

Here you go

3. The next I need checked is...

-3/x+5 - 4/x-5 = 2/ x2-25

I got x= -1 as my answer.
I suppose it's $\frac{-3}{x+5} - \frac{4}{x-5} = \frac{2}{x^2-25}$

If you put the left term on the same denominator, you may have :

$\frac{-3(x-5)-4(x+5)}{x^2-25}=\frac{-7x-5}{x^2-25}$

So you're right