The given: Dividend (x^4-11x^3+15x^2+40x-5)(x4−11x3+15x2+40x−5)
and Divisor (x-5)(x−5)
Synthetic Division:
Start with the dividend,
Arrange the terms from highest to lowest degree:
x^4x4---- x^3x3----x^2x2----x^1x1----x^0x0
Use the numerical coefficients only and the divisor x-5x−5 be equated to zero.
that is x-5=0x−5=0 solving for x: results to x=+5x=+5 the trial divisor.
1 s t Line:1 \ -11 \ +15 \+40 \ \ -5 use trial divisor=+5
2nd Line:0 \ \ +5 \ -30\ -75\-175
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3rd Line:1 \ \ -6 \ \ -15 \ -35\-180
Bring down the first numerical coefficient 1. This number will be multiplied by the trial divisor 5 result is 5 which will be written at the 2nd column under -11. Perform Algebraic addition using -11 and 5 and result is -6 located at the second column of 3rd line.
Next -6 be multiplied by the trial divisor +5, result is -30 to be written at the 3rd column under the +15. Perform Algebraic addition using +15 and -30 and result is -15 located at the 3rd column of 3rd line.
Next -15 be multiplied by the trial divisor +5, result is -75 to be written at the 4th column under the +40. Perform Algebraic addition using +40 and -75 and result is -35 located at the 4th column of 3rd line.
Next -35 be multiplied by the trial divisor +5, result is -175 to be written at the 5th column under the -5. Perform Algebraic addition using -5 and -175 and result is -180 located at the 5th column of 3rd line. And this is the REMAINDER.
Write the answer:
(DIVIDEND)/(DIVISOR)=QUOTIENT+(REMAINDER)/(DIVISOR)
(x^4-11x^3+15x^2+40x-5)/(x-5)=x^3-6x^2-15x-35+(-180)/(x-5)
Have a nice day!!! from the Philippines..
