(x^2+5x-28) divide by (x-3)

Question

you have to divide the polynomial by using long division.

Answer 1

Lamborghini...this is what I understand your problem is...I'll say it in words..

...the quantity x squared plus five x minus twenty-eight divided by the quantity x minus 3....or (x^2+5x-28) divide by (x-3)   I assume you understand that you are dividing a trinomial by a monomial. I will help you solve problems like these...first of all rewrite the equation   (x² + 5x - 28) divide by (x-3) in this form:

                                                        (x² + 5x - 28)    =  ?     or   (x2 + 5x - 28)  over  (x-3)

                                                                      (x-3)

I'm not going to answer the question for you, but will show you how to do these problems with a very similar problem                        (x² + 2x - 24 )         very similar, different values

                                                                              (x -4 )

    Step 1: Look at the trinomial  (x² + 2x - 24 ) =    what this is asking us to do is factor this quantity into to values that when multiplied together will equal    (x² + 2x - 24 ). The more and more you do these kinds of problems, you will recognize that some value/quantity (  ?_Y  ) times (  ?_Z  ) equals (x² + 2x - 24 )  where (  ?_Y  )  equals  something like  ( A + B )  A will equal some value and B will equal another value. B. The same way for ?_Z

...first thing to do is begin with is, this (          )  times  (           ) will equal   (x² + 2x - 24)    the variable is x and in the trinomial it is x² so it will look like  ( x         ) ( x        )  because when we multiple the orange x's we get  x² + 2x - 24

Step 2: we have the x's, now we need to find two factors, two values that when multiplied together will give us 24. So what factors are there of 24: 1, 2, 3, 4, 6, 8, 12: these are                      1  ×  24             2  ×  12          3   ×   8          4   ×  6        right?                             Since there is  a negative in the quantity...find the difference between the factors, like this                24   -  1  =   23             12  -  2   =   10              8  -  3  =  5             6   -  4  =   2    notice that the difference is similar to the coefficient of the middle of  x2 + 2 x - 24  

Step 3: we know the variable is x and the constants are 6 and 4, we just have to put them in the right order, something like    ( x   +  6)( x   -   4 ) , we want the 2 to be positive so the larger the constant HAS to be positive, like above.

Step 4: Rewrite the original equation with the two factors:        (x +  6 )  ( x  -  4 )

                                                                                                                       x  -  4

                       so                         ( x  +  6 ) ( x - 4 )              x  -  4  is cancelled out

                                                             x  -  4

STEP 5:    So the answer is    ( X  +  6 )    now...put your values in the the steps below...and you will have your answer...it is a very similar problem. Now you will be MASTER...

 

Answer 2

you can not factor an x-3 out of x^2+5x-28.  There for you must use long division.

                        4     

      __x_+8 _-_x-3_____________

x-3| x^2+5x-28     start by seeing how many times the first coefficient will go into the first term of the                                                                    polynominal

      -(x^2 -3x)       multiply x-3 by x and subtract the first and second terms.

      __________

               8x-28    repeat until you are at the end of the polynominal

         -   (8x-24)    

             _______

                     -4     as you can see there is a remainder write the remainder added to the end as a                                                                        fraction.

                  -4  

                (x-3)

 

                                        -4 

The answer is x  +  8  +   (X-3)