SOLUTION: use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. x^3+2x^2-11x-12=0;-4 a){3,1

Question 147748: use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
x^3+2x^2-11x-12=0;-4
a){3,1,-4}
b){3.-1.-4}
c){-3,1,-4)
d){-3,-1,-4}
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

First set up the synthetic division table by placing the test zero (which in this case is -4) in the upper left corner and placing the coefficients of the function to the right of the test zero.

-4	\|	1	2	-11	-12
	\|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)

-4	\|	1	2	-11	-12
	\|
		1

Multiply -4 by 1 and place the product (which is -4) right underneath the second coefficient (which is 2)

-4	\|	1	2	-11	-12
	\|		-4
		1

Add -4 and 2 to get -2. Place the sum right underneath -4.

-4	\|	1	2	-11	-12
	\|		-4
		1	-2

Multiply -4 by -2 and place the product (which is 8) right underneath the third coefficient (which is -11)

-4	\|	1	2	-11	-12
	\|		-4	8
		1	-2

Add 8 and -11 to get -3. Place the sum right underneath 8.

-4	\|	1	2	-11	-12
	\|		-4	8
		1	-2	-3

Multiply -4 by -3 and place the product (which is 12) right underneath the fourth coefficient (which is -12)

-4	\|	1	2	-11	-12
	\|		-4	8	12
		1	-2	-3

Add 12 and -12 to get 0. Place the sum right underneath 12.

-4	\|	1	2	-11	-12
	\|		-4	8	12
		1	-2	-3	0

Since the last column adds to zero, we have a remainder of zero. This means that -4 is a solution of the equation

Now lets look at the bottom row of coefficients:

The first 3 coefficients (1,-2,-3) form the quotient

So

Basically factors to

Now lets solve :

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers are:

, or

RELATED QUESTIONS
CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Use synthetic division to show that the... (answered by ilana)

Use synthetic division to show that the number given to the right of the equation is a... (answered by Earlsdon)

Ok this one has completely stumped me: i am only coming up with two answers but the... (answered by scott8148)

Use synthetic division to show that the given x value is a zero of the polynomial. Then... (answered by josgarithmetic)

use synthetic division to show that the given x value is a zero of the polynomial. Then... (answered by josgarithmetic,Edwin McCravy)

4.7 Answer the following questions about the equation below: 12x^3 +53x^2 -34x+5=0 (answered by Boreal)

The volume of the cube shown is 8 cubic centimeters. Cube image has (x-3)(x-3)(x-3) (answered by Boreal)

Use synthetic division to show that x is a solution of the third- degree polymonial... (answered by Edwin McCravy)

Hello, I'm not sure where this problem is supposed to go so I just put it here. Use... (answered by josgarithmetic)