Question

Divide polynomial 3x³ -8x² +x + 7 by x-3 using synthetic division method & write quotient & remainder
plz answer fast and correct and i will mark you as a brainlist​

Answer 1

Write the problem in a division-like format.

To do this:

   Take the constant term of the divisor with the opposite sign and write it to the left.

   Write the coefficients of the dividend to the right.

3x33x2−8x11x07

Step 1

Write down the first coefficient without changes:

3  33−817

Step 2

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

333−83⋅3=9(−8)+9=117

Step 3

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

333−89113⋅1=31+3=47

Step 4

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

333−89113473⋅4=127+12=19

We have completed the table and have obtained the following resulting coefficients: 3,1,4,19.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus, the quotient is 3x2+x+4, and the remainder is 19.

Therefore, 3x3−8x2+x+7x−3=3x2+x+4+19x−3

Answer: 3x3−8x2+x+7x−3=3x2+x+4+19x−3