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Question 22715: Thank you for your help, and I really need it. Please help divide by using synthetic division (4z^5+z^2-4z+9)/(z+2)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! PUT Z+2=0...SO Z=-2
-2....|4.....0......0......1.......-4......9
......|0....-8.....16......-32.....62....-116
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......|4....-8.....16......-31.....-58....-107
HENCE QUOTIENT IS 4Z^4-8Z^3+16Z^2-31Z-58 AND REMAINDER IS -107 WHEN (4z^5+z^2-4z+9) IS DIVIDED BY (z+2)
SEE BELOW FOR EXPLANATION IN SIMILAR PROBLEM
Divide x^3 - 1 by x - 1, x^4 - 1 by x - 1, and x^5 - 1 by x - 1. What is the quotient when x^9 - 1 is divided by x - 1?
1 solutions
Answer 8067 by venugopalramana(454) About Me on 2005-10-22 01:41:44 (Show Source):
there is a procedure for short division called horner's method which can be used here. i shall show you 2 examples ..rest you can do in a similar manner..
first write the given expression in decreasing order of powers listing missing terms also as zeros...
For example x^3-1 = 1*x^3+0*x^2+0*x-1..........(A)
now check if we have the divisor in the form of x+a or x-a or not .we have here x-1 which is in the form x-a...then let x-1 =0 which gives us x=1...(B)
now do the division as follows
write 1 0 0 -1......these are coefficients of powers of x obtained above under (A)from the problem
put 1 as divisor as obtained under (B) above
do as follows
divisor...1|.. 1..0..0..-1......row 1
...........|.. 0..1..1..1.......row 2
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...........|...1..1..1..0 ......row 3
explanation: row 1 has divisor on the left as 1 followed by a seperation bracket..then put coefficients of powers of x obtained above under (A)from the problem in different columns
row 2 ..start with a zero under the coefficient in row 1 in 1st.column..now add the row 1 and row 2 numbers in 1st. column (which are there vertically one below the other )and put the sum under the same column in row 3...here 1+0=1..now multiply this number in row 3 with divisor and put it in row 2 in second column...now add numbers in row 1 and row 2 in column 2 put the sum in row 3 under same column no.2....repeat the procedure till the end
row 3 represents the quotient and remainder...number in last column in row 3 is remainder here it is zero.the other numbers read from right to left give the coefficients of increasing powers of x ...that is the answer on division is 1x^2+1x+1..remainder =0
to explain i am giving another example below...x^2-5x+6 devide by x-3
put x-3 =0 so x=3 is the divisor...
3] 1 -5 6
..... 0 3 -6
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..... 1 -2 0 answer is x-2 and remainder is 0
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