# Use synthetic division to find the quotient and remainder   (3x^3 + 4x^2 - 7x + 6)/(x-3)

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

`3x^3+4x^2-7x+6`  divided by  `x-3`

`f(x)=3x^3+4x^2-7x+6 `

and

`g(x)=x-3`

`g(x)=0`   if  x=3

write  in first row zero of g(x), and coefficients of f(x) indecreasing degree.Below  second column of first row ,write zero of g(x) and multply with element in first column ,write down to third column in second row . Add these column elements in first and second row ,write down in third row.

Let write it as 3 x 3  matrix

`a_11=` zero of g(x)

`a_12=` coefficient of `x^3`  , `x_13=` coefficien of `x^2`  ,... so on

`a_21=a_22=0` , `a_32=a_11` , `a_23=a_11xxa_32` ,

`a_33=a_13+a_23,`  `a_34=a_14+a_24`

and so on.Element in last column in third row is  remainder.

3        3        4        -7          6

9        39        96

-------------------------------------

3        13       32       102

quotient= `3x^2+13x+32`

Remainder=120

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

(3x^3 + 4x^2 - 7x + 6)/(x-3)

x-3=x-a

3,4,-7,6  are resp. coffieints of  x^3 ,x^2,x and constant terms

a      x^3        x^2        x       constant

3       3             4         -7         6        (cofficients and constants)

9         39       196

------------------------------------------------

3             13        32       102

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