Question

Use synthetic division to find the quotient and remainder when is divided by . Specifically, complete the synthetic division table below, and write your answer in the following form: .

Answer 1

Answer:

The calculator will divide the polynomial by the binomial using synthetic division, with steps shown. ... (under the horizontal line). Add the obtained result to the next coefficient of the dividend, and write down the sum.

Answer 2

The quotient and remainder are $\bf 3 {x}^{3} + 13 {x}^{2} - 4x + 2$ and 0 respectively.

Given:

• $3 {x}^{4} + 19 {x}^{3} + 22 {x}^{2} - 6x + 4$
• $x + 2$

To find:

• Perform synthetic division and write quotient and remainder.

Solution:

Step 1:

Perform synthetic division.

Write the coefficients of dividend in RHS and write the value of x from divisor in LHS.

Take 1st coefficients down,

Multiply it with -2 and place the value under coefficient of x³,add\subtract both and place down,repeat the process till end.

-2 ) 3 19 22 -6 4

-6 -26 8 -4

_______________________

3 13 -4 2 0

Thus,

Quotient is

$3 {x}^{3} + 13 {x}^{2} - 4x + 2$

and remainder is 0.

Step 2:

Answer is written in prescribed form can be written as

$\bf 3 {x}^{4} + 19 {x}^{3} + 22 {x}^{2} - 6x + 4 \\ = \bf 3 {x}^{3} + 13 {x}^{2} - 4x + 2 + \frac{0}{x + 2}$

Thus,

By this way synthetic division can be easily performed.

Learn more:

1) (x4-x3+2)÷(x+2) polynomial

Long division

synthetic division

reminder theorem

factor theorem

(Solution)

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2) Divide x4-5x2- 4x by x+3 find the remainder by remainder theorem verify by finding the remainder using synthetic divisio...

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