Question

Find the remainder of (h4 + h2 – 2) ÷ (h + 3).

Answer 1

Step by step solution :

Step  1  :

h4 + h2 - 2 Simplify ——————————— h + 3

Trying to factor by splitting the middle term

 1.1     Factoring  h4 + h2 - 2 

The first term is,  h4  its coefficient is  1 .
The middle term is,  +h2  its coefficient is  1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2 

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   1 .

     -2   +   1   =   -1     -1   +   2   =   1   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  2 
                     h4 - 1h2 + 2h2 - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    h2 • (h2-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (h2-1)
Step-5 : Add up the four terms of step 4 :
                    (h2+2)  •  (h2-1)
             Which is the desired factorization

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