Question

What is the result when 3x^3-x^2-4x+20 is divided by x+2?

Answer 1

Did not paste right..

Answer 2

What is the result when 3x^3-x^2-4X+20 is divided by 2?

Answer 3

Hey Jim

Answer 4

Hey, so it sounds like all you're doing is dividing each term by 2.

I initially thought you were doing polynomial long division and maybe wanted to divide over x+2, but nevermind that thought.

Answer 5

This is synthetic division

Answer 6

Can you post a screenshot?

Answer 7

Sure

Answer 8

Thanks that clears things up.

So first thing we do is write the coefficients of the polynomial
3x^3-x^2-4x+20

It might help to write it as
3x^3-1x^2-4x+20

The coefficients are: 3, -1, -4, 20

Answer 9

Since we're dividing by x+2, this means x+2 = 0 leads to x = -2 being the value we have in the upper left corner of the synthetic division table

Answer 10

What's the next step?

Answer 11

hint: it involves the coefficient 3

Answer 12

3/2?

Answer 13

No it becomes -3

Answer 14

we'll be pulling down the 3 like so

Answer 15

Oh

Answer 16

Multiply the rest by -2?

Answer 17

correct, we multiply that 3 we just pulled down with the -2 in the box
3*(-2) = -6
That -6 will go underneath the next coefficient

Answer 18

what do we do with the -1 and -6?

Answer 19

Subtract?

Answer 20

-7?

Answer 21

close, we add them

Answer 22

Okie

Answer 23

-7 is correct, but we got that result by adding -1 to -6

Answer 24

Yes

Answer 25

then the process of "multiply by the value in the box, write the number under the next coefficient, add straight down" is repeated. You keep repeating until the table is filled out

Answer 26

So the -6 times -2

Answer 27

the -7 we just got will multiply with the -2

Answer 28

Ohh the answer times 2

Answer 29

-14

Answer 30

18

Answer 31

-18 sorry

Answer 32

-7*(-2) = 14

Answer 33

10

Answer 34

Then we add

Answer 35

yep you beat me to it

Answer 36

Hehe

Answer 37

Repeat the process again

Answer 38

10x(-2) = -20

Answer 39

correct

Answer 40

3-7+10 is the answer

Answer 41

Okay I was right

Answer 42

The last item in the bottom row is always the remainder

A remainder of 0 means x+2 is a factor of 3x^3-x^2-4x+20

The quotient is formed by the remaining items in the bottom row

And this indicates 3x^3-x^2-4x+20 = (x+2)(3x^2-7x+10)

You can check this by using the distributive property or the box method

Answer 43

This is actually very useful for my hw too. Thanks jim

Answer 44

No problem

Answer 45

Why is the 3x squared

Answer 46

The values 3, -7, 10 are coefficients

We basically start with the right most item 10 and stick a x^0 onto it, but that's the same as multiplying by 1

The -7 goes with x^1 or just x
The 3 goes with x^2

3x^2 - 7x^1 + 10x^0 = 3x^2 - 7x + 10

If the quotient row had 4 values in it, ignoring the remainder, then the quotient would be some cubic polynomial. The general idea is that if you divide a cubic over a linear polynomial, then the quotient is some quadratic.

In more general terms, we basically just subtract the largest exponents to figure out what the quotient will look like (what the degree of the quotient is)

Answer 47

Okay got it

Answer 48

Thank you Jim

Answer 49

no problem