SOLUTION: Please help me out, I don't know how to begin to approach these. :[ Thanks so much Divide using synthetic division. a) (x^2 + 7x + 12) divided by (x + 4) b) (x^4 - 7x^2 + 9x

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me out, I don't know how to begin to approach these. :[ Thanks so much Divide using synthetic division. a) (x^2 + 7x + 12) divided by (x + 4) b) (x^4 - 7x^2 + 9x       Log On


   



Question 147620: Please help me out, I don't know how to begin to approach these. :[
Thanks so much
Divide using synthetic division.
a) (x^2 + 7x + 12) divided by (x + 4)
b) (x^4 - 7x^2 + 9x - 10) divided by (x - 2)
c) (2x^4 - 11x^3 + 15x^2 + 6x - 18) divided by (x - 3)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started.


a)



Let's simplify this expression using synthetic division


Start with the given expression %28x%5E2+%2B+7x+%2B+12%29%2F%28x%2B4%29

First lets find our test zero:

x%2B4=0 Set the denominator x%2B4 equal to zero

x=-4 Solve for x.

so our test zero is -4


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.
-4|1712
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
-4|1712
|
1

Multiply -4 by 1 and place the product (which is -4) right underneath the second coefficient (which is 7)
-4|1712
|-4
1

Add -4 and 7 to get 3. Place the sum right underneath -4.
-4|1712
|-4
13

Multiply -4 by 3 and place the product (which is -12) right underneath the third coefficient (which is 12)
-4|1712
|-4-12
13

Add -12 and 12 to get 0. Place the sum right underneath -12.
-4|1712
|-4-12
130

Since the last column adds to zero, we have a remainder of zero. This means x%2B4 is a factor of x%5E2+%2B+7x+%2B+12

Now lets look at the bottom row of coefficients:

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

x+%2B+3


So %28x%5E2+%2B+7x+%2B+12%29%2F%28x%2B4%29=x+%2B+3 where x%3C%3E-4

You can use this online polynomial division calculator to check your work






Let's simplify this expression using synthetic division


Start with the given expression %28x%5E4+-+7x%5E2+%2B+9x+-+10%29%2F%28x-2%29

First lets find our test zero:

x-2=0 Set the denominator x-2 equal to zero

x=2 Solve for x.

so our test zero is 2


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.(note: remember if a polynomial goes from 1x%5E4 to -7x%5E2 there is a zero coefficient for x%5E3. This is simply because x%5E4+-+7x%5E2+%2B+9x+-+10 really looks like 1x%5E4%2B0x%5E3%2B-7x%5E2%2B9x%5E1%2B-10x%5E0
2|10-79-10
|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
2|10-79-10
|
1

Multiply 2 by 1 and place the product (which is 2) right underneath the second coefficient (which is 0)
2|10-79-10
|2
1

Add 2 and 0 to get 2. Place the sum right underneath 2.
2|10-79-10
|2
12

Multiply 2 by 2 and place the product (which is 4) right underneath the third coefficient (which is -7)
2|10-79-10
|24
12

Add 4 and -7 to get -3. Place the sum right underneath 4.
2|10-79-10
|24
12-3

Multiply 2 by -3 and place the product (which is -6) right underneath the fourth coefficient (which is 9)
2|10-79-10
|24-6
12-3

Add -6 and 9 to get 3. Place the sum right underneath -6.
2|10-79-10
|24-6
12-33

Multiply 2 by 3 and place the product (which is 6) right underneath the fifth coefficient (which is -10)
2|10-79-10
|24-66
12-33

Add 6 and -10 to get -4. Place the sum right underneath 6.
2|10-79-10
|24-66
12-33-4

Since the last column adds to -4, we have a remainder of -4. This means x-2 is not a factor of x%5E4+-+7x%5E2+%2B+9x+-+10
Now lets look at the bottom row of coefficients:

The first 4 coefficients (1,2,-3,3) form the quotient

x%5E3+%2B+2x%5E2+-+3x+%2B+3

and the last coefficient -4, is the remainder, which is placed over x-2 like this

-4%2F%28x-2%29



Putting this altogether, we get:

x%5E3+%2B+2x%5E2+-+3x+%2B+3%2B-4%2F%28x-2%29

So %28x%5E4+-+7x%5E2+%2B+9x+-+10%29%2F%28x-2%29=x%5E3+%2B+2x%5E2+-+3x+%2B+3%2B-4%2F%28x-2%29 where x%3C%3E2

which looks like this in remainder form:
%28x%5E4+-+7x%5E2+%2B+9x+-+10%29%2F%28x-2%29=x%5E3+%2B+2x%5E2+-+3x+%2B+3 remainder -4 where x%3C%3E2


You can use this online polynomial division calculator to check your work