Answer: The quotient is [tex]3x^3+6x^2+8x+24+\frac{47}{x-2}[/tex].
Explanation:
The given dividend is,
[tex]3x^4-4x^2+8x-1[/tex]
The coefficients of [tex]x^4,x^3,x^2,x[/tex] and constant are 3, 0, 4,8,-1.
The divisor is,
[tex]x-2[/tex]
The divisor is in the form of x-c so the value of c is 2. Write the number 2 and the coefficient of dividend in top row as shown in the below figure.
Write first coefficient 3 as it is, in bottom row.
Multiply 2 by 3 and write the result (i.e., 6) in middle row below the coefficient of second term.
Add 0 and 6, and write the result ( i.e., 6) in bottom line.
Multiply 2 by 6 and write the result (i.e., 12) in middle row below the coefficient of third term.
Add -4 and 12, and write the result ( i.e., 8) in bottom line.
Multiply 2 by 8 and write the result (i.e., 16) in middle row below the coefficient of fourth term.
Add 8 and 16, and write the result ( i.e., 24) in bottom line.
Multiply 2 by 24 and write the result (i.e., 48) in middle row below the coefficient of fifth term.
Add -1 and 48, and write the result ( i.e., 47) in bottom line.
Now the first four element of bottom line shows the coefficient of quotient and the last element shows the remainder.
The degree of dividend is 4 so degree of quotient must be one less than the degree of the dividend.
Degree of the quotient is 3.
[tex]Q=3x^3+6x^2+8x+24+\frac{47}{x-2}[/tex]
