Any help with these problems?

[PantherSnap]

I'm learning synthetic division in my math class at the moment and here are the two problems:

(-5x3 - 10x2 + 16x + 3) ÷ (x + 3)

(x2 + 11x + 20) ÷ (x + 8)

I'm having trouble with the first one, but for the second one I ended up getting x+3x-4/x+8

 

[JeffM]

With respect to the second, here is how you can check your own work

[MATH]x^2 + 11x + 20 \div x + 8 = x + 3x - \dfrac{4}{x + 8} \implies \\ (x + 8 ) * \left ( x + 3x - \dfrac{4}{x + 8} \right ) = x(x + 8) + 3x(x + 8) - 4 = \\ x^2 + 8x + 3x^2 + 24x - 4 = 4x^2 + 32x - 4 \ne x^2 + 11x + 20.[/MATH]So there is an error. It is a very simple error. Can you find it?

With respect to the first problem, what is the very first number you "brought down"?

 

[Otis]

… (x2 + 11x + 20) ÷ (x + 8)

… I ended up getting x+3x-4/x+8

Hi PantherSnap. We use the caret symbol ^ to show exponents. Like this:

x^2 + 11x + 20

Also, when a denominator is more than a single number or symbol, we need to type grouping symbols around it (otherwise, the meaning is not clear).

x + 3 - 4/(x + 8)

Your answer above is almost correct, but you've misinterpreted the bottom row of the synthetic division.

-8   │   1   11   20
             -8  -24
         1    3   -4

The 1 is the coefficient of the x-term, the 3 is the constant, and the -4 is the remainder.

x + 3 - 4/(x + 8)

You may check this answer; multiply it by the divisor, to get the dividend.

(x + 8)(x + 3 - 4/[x + 8]) = x^2 + 11x + 20

Please show your work on the first exercise. Thanks.

?

 

[HallsofIvy]

I strongly recommend that you use the " ^" character to show exponents- "x3" is too easily confused with "\(\displaystyle x_3\)" (which would be better written as "x_3"). Also please use parentheses: the correct answer to the second problem is x+3- 4/(x+ 8). Was the "3x"a typo?


It's been along time since I used "synthetic division" (and I never really liked it). Using "regular division for the first problem, -5x^3- 10x^2+ 16x+ 3 divided by x+ 3, x divides into "-5x^3" -5x^2 times. Multiply x+ 3 by -5x^2 to get -5x^3- 15x^2 and subtract that from the first dividend: -5x^3- 10x^2+ 16x+ 3-(-5x^3- 15x^2)= 5x^2+ 16x+ 3.

Now x divides into 5x^2 5x times. 5x times x+3 is 5x^2+ 15x. Subtract that from 5x^2+ 16x+ 3: 5x^2+ 16x+ 3- (5x^2+ 15x)= x+ 3. Of course x+ 3 divides into that exactly once.

-5x^3- 10x^2+ 16x+ 3 divide by x+ 3 is -5x^2+ 5x+ 1.

 

[PantherSnap]

I was wondering if i can get a long division method written out?

 

[Deleted member 4993]

I was wondering if i can get a long division method written out?

Go to google and do a search with keywords "polynomial division"

You'll find thousands of websites with answers......

 

[JeffM]

I was wondering if i can get a long division method written out?

But you are being asked to learn synthetic division so why try a different method?

Please answer my previous question. What is the FIRST number you bring down?

[MATH]-3 | \underline {-5 \ \ -10 \ \ +16 \ \ +3}[/MATH]