Question

use synthetic division to find (x^5 + x^3 - 13x^2 + 12) ÷ (x - 2). write your answer in the form q(x) + r/d(x), where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. simplify any fractions.

Explanation:

Step1: Set up synthetic division

The divisor is $x - 2$, so we use $c = 2$. The dividend coefficients are $1,0,1,-13,0,12$ (for $x^{5}+0x^{4}+x^{3}-13x^{2}+0x + 12$).

2	1	0	1	-13	0	12
	1

Step2: Bring down the first coefficient

Bring down the first coefficient 1.

2	1	0	1	-13	0	12
	1

Step3: Multiply and add

Multiply 2 by 1 to get 2, add to 0 to get 2.

2	1	0	1	-13	0	12
	1	2

Step4: Repeat multiplication - addition

Multiply 2 by 2 to get 4, add to 1 to get 5.

2	1	0	1	-13	0	12
	1	2	5

Step5: Continue the process

Multiply 2 by 5 to get 10, add to - 13 to get - 3.

2	1	0	1	-13	0	12
	1	2	5	- 3

Step6: Keep going

Multiply 2 by - 3 to get - 6, add to 0 to get - 6.

2	1	0	1	-13	0	12
	1	2	5	- 3	- 6

Step7: Final multiplication - addition

Multiply 2 by - 6 to get - 12, add to 12 to get 0.

2	1	0	1	-13	0	12
	1	2	5	- 3	- 6	0

Answer:

$x^{4}+2x^{3}+5x^{2}-3x - 6+\frac{0}{x - 2}=x^{4}+2x^{3}+5x^{2}-3x - 6$