SOLUTION: What is the remainder when 4x3 + 5x2 - 13x - 7 is divided by x

SOLUTION: What is the remainder when 4x3 + 5x2 - 13x - 7 is divided by x - 2? I came up with -33 is this correct?

Question 90279: What is the remainder when 4x3 + 5x2 - 13x - 7 is divided by x - 2?

I came up with -33 is this correct?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given polynomial

First lets find our test zero:

Set the denominator equal to zero
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.

2	\|	4	5	-13	-7
	\|

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

2	\|	4	5	-13	-7
	\|
		4

Multiply 2 by 4 and place the product (which is 8) right underneath the second coefficient (which is 5)

2	\|	4	5	-13	-7
	\|		8
		4

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

2	\|	4	5	-13	-7
	\|		8
		4	13

Multiply 2 by 13 and place the product (which is 26) right underneath the third coefficient (which is -13)

2	\|	4	5	-13	-7
	\|		8	26
		4	13

Add 26 and -13 to get 13. Place the sum right underneath 26.

2	\|	4	5	-13	-7
	\|		8	26
		4	13	13

Multiply 2 by 13 and place the product (which is 26) right underneath the fourth coefficient (which is -7)

2	\|	4	5	-13	-7
	\|		8	26	26
		4	13	13

Add 26 and -7 to get 19. Place the sum right underneath 26.

2	\|	4	5	-13	-7
	\|		8	26	26
		4	13	13	19

Since the last column adds to 19, we have a remainder of 19. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 3 coefficients (4,13,13) form the quotient

and the last coefficient 19, is the remainder.

So the remainder is 19

note: it looks like you added -26 and -7 to get -33. Instead you should add 26 and -7 to get 19

You can use this online polynomial division calculator to check your work
RELATED QUESTIONS
A positive number when divided by 35 gives the remainder 33. What will the remainder be... (answered by richwmiller)

When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by... (answered by ikleyn)

Using synthetic division, what is the quotient and the remainder when (2x^3-3x+1) is... (answered by josgarithmetic,ikleyn)

Can I get more assistance with this problem, thanks! Find the quotient and remainder... (answered by stanbon,jim_thompson5910)

when x^7+kx-2 is divided by x-1, the remainder is 7. what is the value of... (answered by user_dude2008,Syzy144)

What is that number , when that number is divided by 9 the remainder is 8 , when that... (answered by AnlytcPhil)

Hello can someone help with this problem? What is the remainder when x^7-x^6+x^5-x^4+4 (answered by stanbon)

When a number n is divided by 7, the remainder is 2. What is the remainder when 2n+1 is... (answered by Edwin McCravy)

Can someone please help me with this problem? Multiply: 3y^2+13y+14 divided by y^2+3y+2... (answered by stanbon)