Polynomial division help me i have a test coming soon. 10 points?

Question

1. (2x^2+10x+12)\(x+3)

2. (6x^3-16x^2+17x-6) \ (3x-2)

3. X^3+4x^2-3x-12

_____________

X^2-3

4. (3X^3+17X^2 +15X+2) \ (X+5)

5. -X^3+75X-250

----------------------

X+10

Answer 1

1. (2x^2+10x+12)\(x+3)

    = (x + 3) (2x + 4)

2. (6x^3-16x^2+17x-6) \ (3x-2)

    = (3x-2) (2x^2 - 4x + 3)

3. (X^3+4x^2-3x-12) / (x^2 - 3)

   = (x^2 - 3) ( x + 4)

4. (3X^3+17X^2 +15X+25) \ (X+5) ----- I think this equation should be + 25 not only 2.

   = (x + 5) (3x^2 + 2x + 5)

5. (-X^3+75X-250) / (x + 10)

    = -(X^3 - 75x + 250) / (x + 10)

    = -(x + 10) (x^2 - 10x + 25)

Hope this may help you,

Thank you.

Answer 2

Have you learnt how to do long division using polynomials?

If that's what you need i'm sure somewhere on the internet explains it

i don't really understand what you've written above... are they just questions?

Answer 3

Q.1:

First factorise it then simplify

2x^2 + 10x + 12

= 2(x^2 + 5x+6)

=2(x^2 + 3x+2x+6)

=2{x(x+3) +2(x+3)}

=2(x+3)(x+2)

Now, (2x^2+10x+12)/(x+3)

= 2(x+3)(x+2)/(x+3)

=2(x+2) <==ANSWER

similarly we can proceed for the rest  problems.

here we go.

Q.2:

6x^3 -16x^2 + 17x - 6

= 6x^3 - 4x^2 - 12x^2 + 8x + 9x - 6

=2x^2(3x-2)-4x(3x-2)+3(3x-2)

=(3x-2)(2x^2-4x+3) .........=> (vanishing factor)

Now, (6x^3 - 16x^2 + 17x - 6)/(3x-2)

= (3x-2)(2x^2-4x+3)/(3x-2)

=(2x^2-4x+3) <==ANSWER

Q.3:

x^3 + 4x^2 - 3x - 12

= x^2(x +4) - 3(x+4)

=(x+4)(x^2 - 3)

Now, (x^3 +4x^2 -3x-12)/(x^2 - 3)

= (x+4)(x^2 -3)/(x^2 -3)

= (x+4) <==ANSWER

Now, similarly solve rest problems.

Answer 4

I can't really explain this in the internet.

But, those questions can be solve by using "Horner" method or :

x+3 / 2x^2+10x+12    ----->  turn (x) to (2x^2) by multiplying it with (2x)

         2x^2+6x         _          if you multiply (x) that means(2x+3)should

                  4x+12  -----|       be multiplied by (2x) as well.

                  4x+12   _  |       (x+3)2x=2x^2+6x

                         0       |

                                  |___>  turn(x) to 4x by using the same method.

                                             (x+3)4=4x+12

The result = 2x + 4 ( add all of the multiplication factors)

Do the rest alone. I'm tired

        

Answer 5

                 2x+4

       ---------------------

x+3 ) 2x^2+10x+12

        2x^2+6x

        ------------

                 4x+12

                 4x+12

If you understand what is happening here, you can solve the remaining 4.