SOLUTION: If {{{P(x)=4x^4 - 12x^3 - 70x^2 - 9x + 8}}} find P(6) using synthetic division and the remainder theorem

Question 138656: If find P(6) using synthetic division and the remainder theorem
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to evaluate P(6), simply use synthetic division

Since we want to find P(6), our test zero is 6

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.

6	\|	4	-12	-70	-9	8
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 4)

6	\|	4	-12	-70	-9	8
	\|
		4

Multiply 6 by 4 and place the product (which is 24) right underneath the second coefficient (which is -12)

6	\|	4	-12	-70	-9	8
	\|		24
		4

Add 24 and -12 to get 12. Place the sum right underneath 24.

6	\|	4	-12	-70	-9	8
	\|		24
		4	12

Multiply 6 by 12 and place the product (which is 72) right underneath the third coefficient (which is -70)

6	\|	4	-12	-70	-9	8
	\|		24	72
		4	12

Add 72 and -70 to get 2. Place the sum right underneath 72.

6	\|	4	-12	-70	-9	8
	\|		24	72
		4	12	2

Multiply 6 by 2 and place the product (which is 12) right underneath the fourth coefficient (which is -9)

6	\|	4	-12	-70	-9	8
	\|		24	72	12
		4	12	2

Add 12 and -9 to get 3. Place the sum right underneath 12.

6	\|	4	-12	-70	-9	8
	\|		24	72	12
		4	12	2	3

Multiply 6 by 3 and place the product (which is 18) right underneath the fifth coefficient (which is 8)

6	\|	4	-12	-70	-9	8
	\|		24	72	12	18
		4	12	2	3

Add 18 and 8 to get 26. Place the sum right underneath 18.

6	\|	4	-12	-70	-9	8
	\|		24	72	12	18
		4	12	2	3	26

Since the last column adds to 26, we have a remainder of 26. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 4 coefficients (4,12,2,3) form the quotient

and the last coefficient 26, is the remainder.

According to the remainder theorem, the remainder is equal to P(6)

Answer:

So P(6)=26
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