# uhhh... polynomial long division??

#### Kneecoal

10+ Year Member
who? what? how?

(t^2 + 2t + 4) / (t+1)

topscore talks about subtracting (t^2 + t) from the first parentheses, and then subtracting the (t+1) from the remainder (t+4) to get the answer of

(t+1) + 3/(t+1)

sure i can smile and nod the whole time, but i don't understand the "why" of any of it, and i don't ever really remember learning this... can someone please try and explain a little? muchos gracias!

#### ohohitsmagic08

Its kinda hard to explain via typing but I'll give it a shot.

You basically think like you are dividing normally
(t+1)*X=t^2+2t+4
If X=t, then you get t^2+t
so subtract (t^2+t) from t^2+2t+4 and you get t+4
Now (t+1)*X=t+4
If x=1, then you get t+1
so subtract t+1 from t+4 and you get 3 as the remainder.
Now (t+1)*X=3
If x=(3/(t+1)) then you get 3.

who? what? how?

(t^2 + 2t + 4) / (t+1)

topscore talks about subtracting (t^2 + t) from the first parentheses, and then subtracting the (t+1) from the remainder (t+4) to get the answer of

(t+1) + 3/(t+1)

sure i can smile and nod the whole time, but i don't understand the "why" of any of it, and i don't ever really remember learning this... can someone please try and explain a little? muchos gracias!

#### Popat Lal

5+ Year Member
Alright I didn't do what it sed in the book. but this is what I did.

First of all, I used the quadratic formula for (t^2)+2t+4. (-b +/-square root((b^2)-4ac))/2a)

that got me to the result that of "-1 +/- square root(3)" for the value of t. so then (t^2)+2t+4 = (t-1 + square root(3) (t-1 - square root(2)). Notice the same variable of "t-1." so you factor out the "t-1" part and watchu get is (t-1)(+/- square root (3)). Now compare to the original equation.

(t^2)+2t+4/(t-1)= (t-1)(+/- square root (3))/(t-1). the "t-1's" cancels out and you have ur answer (+/- square root (3)

-hope the wording wasn't too confusing

#### UCB05

who? what? how?

(t^2 + 2t + 4) / (t+1)

topscore talks about subtracting (t^2 + t) from the first parentheses, and then subtracting the (t+1) from the remainder (t+4) to get the answer of

(t+1) + 3/(t+1)

sure i can smile and nod the whole time, but i don't understand the "why" of any of it, and i don't ever really remember learning this... can someone please try and explain a little? muchos gracias!

*checking thread date* ah, not 3 yrs old.

Assuming you know long division, it's the same concept, but with dual terms. Since the first term of the denominator is t and the first term of the numerator is t^2, you divide by a factor of t.

That factor is distributed throughout the denominator, so you get (t^2+t). Subtract that from the numerator t^2+2t+4 to get a remainder of t+4. (t+1) divides into (t+4) by a factor of 1. Subtract and you're left with 3. Since 3 is not divisible by (t+1) by any multiple of t or whole number, you're left with a remainder of 3/(t+1) after dividing out a total of t+1.

It might be easier to visualize if you set up the whole long division problem. Pls excuse the chicken scratch

#### Kneecoal

10+ Year Member
ok, that helped some, but i have a few more questions

when you had x = t for the first part, would you always multiply the "(t+1)" part by the variable? as in, x'll never be something other than the variable?

same kind of question for the second part where you had x = 1 - do you always multiply by 1?

is the (t+1) in the answer the same (t+1) you get when you did (t+1)*x = (t+4)?

and then in the second part of the answer, the 3/(t+1) --> is the (t+1) the original (t+1) that you're dividing by? or is it the (t+1) you got when you did the (t+1)*x = t+4? or are you always going to get the divisor as part of your answer?

hopefully that wasn't too confusing, but the "2" t+1's are messing me up i think.

thanks!

#### Kneecoal

10+ Year Member
*checking thread date* ah, not 3 yrs old.

Assuming you know long division, it's the same concept, but with dual terms. Since the first term of the denominator is t and the first term of the numerator is t^2, you divide by a factor of t.

That factor is distributed throughout the denominator, so you get (t^2+t). Subtract that from the numerator t^2+2t+4 to get a remainder of t+4. (t+1) divides into (t+4) by a factor of 1. Subtract and you're left with 3. Since 3 is not divisible by (t+1) by any multiple of t or whole number, you're left with a remainder of 3/(t+1) after dividing out a total of t+1.

It might be easier to visualize if you set up the whole long division problem. Pls excuse the chicken scratch
lol to the "checking the date." nice.

thanks, this was a really good explanation, especially the chicken scratch!