I need help understanding the polynomials division problems
with exponents.
14y+8y˛+ył+12 ÷ 6+y
First rearrange the terms of both so that the
powers of y are descending and the constant is
on the far right:
ył + 8y˛ + 14y + 12 ÷ y + 6
Write this:
y + 6)ył + 8y˛ + 14y + 12
Divide the y on the far left into the ył,
getting y˛, so write that on top right above
the y˛ in the term 8y˛:
y˛
y + 6)ył + 8y˛ + 14y + 12
Now multiply that y˛ by both the y and the 6,
getting ył + 6y˛ and write than inder the ył + 8y
write that underneath and
y˛
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
Now subtract the 8y˛ MINUS 6y˛ gives 2y˛, so write
that under the line. (When you subrtact the ył MINUS
ył you just get 0, so you don't write anything under
that:
y˛
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛
Now you bring down the + 14y˛
y˛
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
Now divide the y on the far left into the
2y˛ at the bottom, getting 2y, which you write
as + 2y above the top line above the + 14y
y˛ + 2y
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
Next you multiply the 2y by the y + 6, getting
2y˛ + 12y. Write that at the bottom and draw
a line under it:
y˛ + 2y
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
Subtract 14y MINUS 12y getting 2y, write that
under the line. Don't write anything under
the 2y˛ MINUS 2y˛ because that's just 0.
y˛ + 2y
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y
Bring down the + 12
y˛ + 2y
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
Divide the y on the far left into the 2y at
the bottom, getting 2. Write + 2 above the
top line, above the + 12
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
Multiply the 2 by the y + 6, getting 2y + 12. Write
that at the bottom and underline it:
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
When you subtract you get 0. So you can
write 0 at the bottom if you like:
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
0
The remainder is 0, so the quotient (answer)
is y˛ + 2y + 2
It is important to keep like powers of x vertically
straight.
Notice that the ył's are
lined up straight vertically:
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
0
Notice that the y˛'s are
lined up straight vertically:
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
0
Notice that the y's are lined up vertically:
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
0
And the constant numbers are also lined up
vertically.
y˛ + 2y + 2
y + 6)ył + 8y˛ + 14y + 12
ył + 6y˛
2y˛ + 14y
2y˛ + 12y
2y + 12
2y + 12
0
I point this out because it is important to keep
like terms lined up vertically when dividing
polynomials.
Edwin
