SOLUTION: 4x^3-x^2-13x+10 divided by 4x-5

Question 104510This question is from textbook College Algebra: Concepts and Models
: 4x^3-x^2-13x+10 divided by 4x-5 This question is from textbook College Algebra: Concepts and Models

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's simplify this expression using synthetic division

Start with the given expression

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is 5/4

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.

5/4	\|	4	-1	-13	10
	\|

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

5/4	\|	4	-1	-13	10
	\|
		4

Multiply 5/4 by 4 and place the product (which is 5) right underneath the second coefficient (which is -1)

5/4	\|	4	-1	-13	10
	\|		5
		4

Add 5 and -1 to get 4. Place the sum right underneath 5.

5/4	\|	4	-1	-13	10
	\|		5
		4	4

Multiply 5/4 by 4 and place the product (which is 5) right underneath the third coefficient (which is -13)

5/4	\|	4	-1	-13	10
	\|		5	5
		4	4

Add 5 and -13 to get -8. Place the sum right underneath 5.

5/4	\|	4	-1	-13	10
	\|		5	5
		4	4	-8

Multiply 5/4 by -8 and place the product (which is -10) right underneath the fourth coefficient (which is 10)

5/4	\|	4	-1	-13	10
	\|		5	5	-10
		4	4	-8

Add -10 and 10 to get 0. Place the sum right underneath -10.

5/4	\|	4	-1	-13	10
	\|		5	5	-10
		4	4	-8	0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 3 coefficients (4,4,-8) form the quotient

Notice in the denominator , the x term has a coefficient of 4, so we need to divide the quotient by 4 like this:

So

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

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