Consider two polynomials f(x) and g(x), if we divide f(x) by g(x), we have to follow the given instruction.
Problem 1 :
(5x^{6} – 16x^{5} – 11x^{4} + 22x^{3} + 14x^{2} – 4x + 9) ÷ (x^{2} - 4x + 2)
Solution :
Let f(x) = 5x^{6} – 16x^{5} – 11x^{4} + 22x^{3} + 14x^{2} – 4x + 9
and
g(x) = x^{2} - 4x + 2
Step 1 :
Divide 5x^{6} by x^{2}, so 5x^{6}/x^{2} ==> 5x^{4}
Put 5x^{4 }at the top. Now, multiply 5x^{4} by (x^{2} - 4x + 2)
5x^{4} (x^{2} - 4x + 2) = 5x^{6} - 20x^{5} + 10x^{4}
Write 5x^{6} - 20x^{5} + 10x^{4 }below the given polynomial and then subtract.
Step 2 :
After subtraction, we will have a polynomial, take the first term from inside.
Here 4x^{5} should be divided by x^{2}
4x^{5}/x^{2} ==> 4x^{3}
Now, multiply 4x^{3 }by (x^{2} - 4x + 2)
4x^{3 }(x^{2} - 4x + 2) = 4x^{5} - 16x^{4} + 8x^{3}
Subtract this polynomial from the previous one.
Repeat the process until, we receive degree of the remainder be lesser than to degree of dividend.
Note :
If the order of the given polynomial is rearranged, then write it in the correct order and start division.
IF any term is missing replace it by 0 and then divide.
Problem 1 :
(6x^{4} – 30x^{2} + 24) ÷ (2x^{2} – 8)
Solution :
(6x^{4} – 30x^{2} + 24) ÷ (2x^{2} – 8)
Quotient = 3x^{2} – 3
Remainder = 0
Problem 2 :
(3x^{5} + 4x^{3} – 5x + 8) ÷ (x^{2} + 3)
Solution :
(3x^{5} + 4x^{3} – 5x + 8) ÷ (x^{2} + 3)
Quotient = 3x^{3} – 5x
Remainder = 10x + 8
Problem 3 :
(x^{5} + 2x^{4} + x^{3} – x^{2} – 22x + 15) ÷ (x^{2} + 2x – 3)
Solution :
Quotient = x^{3} + 4x - 9
Remainder = 8x - 12
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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