# Long division method of Algebraic expressions

#### NormalKid

I actually know How to divide an algebraic expression using the long division method.But this one,I have no idea how to do .
I tried to do by rearranging the term but in vain .Someone please help me out here.

t4 -3tq+t+5 by t-1 BY LONG DIVISION METHOD

Thank you

#### skeeter

MHF Helper
I actually know How to divide an algebraic expression using the long division method.But this one,I have no idea how to do .
I tried to do by rearranging the term but in vain .Someone please help me out here.

t4 -3tq+t+5 by t-1 BY LONG DIVISION METHOD
what is q in the second term?

3 x t x q
3tq

sorry,what?

#### Deveno

MHF Hall of Honor
we can start by looking at the leading terms:

t x ? = t4.

clearly we need t3, so our first "go-round" is to multiply t - 1 by t3, and subtract the result from t4 - 3tq + t + 5.

note we can re-write this as:

t4 + 0t3 + 0t2 + (1 - 3q)t + 5.

now (t - 1)(t3) = t4 - t3, and:

t4 + 0t3 + 0t2 + (1 - 3q)t + 5 - (t4 - t3) = t3 + 0t2 + (1 - 3q)t + 5

we've "reduced the degree by one".

again, just looking at the leading terms we see we need to multiply t - 1 by t2, and subtract, so (t - 1)t2 = t3 - t2, and:

t3 + 0t2 + (1 - 3q)t + 5 - (t3 - t2) = t2 + (1 - 3q)t + 5

now we need to multiply t - 1 by t, and subtract: (t - 1)t = t2 - t, and:

t2 + (1 - 3q)t + 5 - (t2 - t) = (2 - 3q)t + 5

here, we need to multiply by 2 - 3q (this will be the "last go-round"), and (t - 1)(2 - 3q) = (2 - 3q)t - (2 - 3q). another subtraction:

(2 - 3q)t + 5 - ((2 - 3q)t - (2 - 3q)) = 5 + (2 - 3q) = 7 - 3q.

now, without knowing what "q" is, this is as far as we can go.

what we've done is shown that:

t4 - 3tq + t + 5 = (t3 + t2 + t + (2 - 3q))(t - 1) + 7 - 3q.

the quotient is: t3 + t2 + t + (2 - 3q)

the remainder is: 7 - 3q.

#### NormalKid

can I just see the work-out?Because Its very hard for me to read and understand. And can you just explain the splitting up of -3tq?

#### MarkFL

Polynomial long division is difficult at best to display using LaTeX.

#### NormalKid

ok.
Can you explain the splitting up of -3tq and why we split that?Sorry I am just a beginner.

#### MarkFL

Are you talking about where $$\displaystyle -3tq+t$$ is written as $$\displaystyle (1-3q)t$$?

#### NormalKid

never mind.I understood the answer.Thank you Mark and Deveno