Question

use synthetic division to find the result when x³ - 27x + 10 is divided by x - 5. if there is a remainder, express the result in the form q(x)+r/(x - 5).

Explanation:

Step1: Set up synthetic - division

The divisor is \(x - 5\), so we use \(c = 5\) in synthetic - division. The dividend is \(x^{3}-27x + 10\), which can be written as \(1x^{3}+0x^{2}-27x + 10\). We set up the synthetic - division as follows:

5	1	0	- 27	10

Step2: Bring down the first coefficient

Bring down the first coefficient 1:

5	1	0	- 27	10
	1

Step3: Multiply and add

Multiply 5 by 1 to get 5, and add to the second coefficient 0: \(0 + 5=5\).

5	1	0	- 27	10
	1	5

Then multiply 5 by 5 to get 25, and add to the third coefficient - 27: \(-27+25=-2\).

5	1	0	- 27	10
	1	5	- 2

Next, multiply 5 by - 2 to get - 10, and add to the fourth coefficient 10: \(10+( - 10)=0\).

5	1	0	- 27	10
	1	5	- 2	0

Step4: Write the result

The numbers on the bottom row represent the coefficients of the quotient polynomial. The quotient is \(x^{2}+5x - 2\) and the remainder is 0.

Answer:

\(x^{2}+5x - 2\)