What is the quotient (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?

The quotient is .

Explanation:

The given dividend is,

The coefficients of and constant are 3, 0, 4,8,-1.

The divisor is,

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.

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