DIVISION OF POLYNOMIALS
4t^{5} + 6t^{3} + 8 ÷ 2t^{2}
In the above case the divisor,
2t^{2} ,is one term and hence each term in 4t^{5} + 6t^{3} + 8 can be
divided individually.
 4t^{5} / 2t^{2} = 2t^{5  2} = 2t^{3}
 6t^{3} /2t^{2} = 3t^{3  2} = 3t
 8 / 2t^{2} = 4 / t^{2}
4t^{5} + 6t^{3} + 8 ÷ 2t^{2} =
4t^{5} / 2t^{2} + 6t^{3} /2t^{2} + 8 / 2t^{2}
= 2t^{5  2} + 3t^{3  2} + 4 / t^{2} = 2t^{3}
+ 3t + 4 / t^{2}
When the divisor is two or more terms the division is a little
more difficult to do. For example:
(x^{2 } 4x  21) ÷ (x + 3)
(x^{2 }  4x  21) is called the dividend and (x + 3) is called the
divisor.
The first term of the dividend x^{2} , is divided by
the first term of the divisor, x.
 x^{2} ÷ x = x
The divisor, (x + 3) is multiplied by x and the result
subtracted from the dividend.
 x(x + 3) = x^{2} + 3x
 (x^{2 }  4x  21)  (x^{2 } + 3x)
= x^{2 }  4x  21  x^{2 }  3x = 7x  21
Next the first term of the answer 7x,
is divided by the first term of the divisor, x.
 7x ÷ x = 7
The answer 7 is multiplied by the divisor
(x + 3).
 7(x + 3) = 7x  21
This is subtracted
from the answer from the first division (7x  21)
 Therefore (7x  21)  (7x  21) = 7x  21 + (7x + 21)
= 7x  21 + 7x + 21 = 0
So the answer for the division problem

(x^{2 } 
4x  21) ÷ (x + 3) is x  7
You can prove this answer is correct by multiplying (x + 3)(x  7)
If the answer is (x^{2 } 
4x  21) then you divided correctly.
Try these problems:
(x^{2} + 13x + 36) ÷ ( x + 9)
answer
(4x^{3} + 5x^{2} + 2x + 4) ÷ (x + 2)
answer
return