Question

factorise -80h+5h²+320​

Answer 1

(80h +  5h2) +  320

Pull out like factors :

  5h2 + 80h + 320  =   5 • (h2 + 16h + 64)

Factoring  h2 + 16h + 64  

The first term is,  h2  its coefficient is  1 .

The middle term is,  +16h  its coefficient is  16 .

The last term, "the constant", is  +64  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 64 = 64  

Step-2 : Find two factors of  64  whose sum equals the coefficient of the middle term, which is   16 .

     -64    +    -1    =    -65  

     -32    +    -2    =    -34  

     -16    +    -4    =    -20  

     -8    +    -8    =    -16  

     -4    +    -16    =    -20  

     -2    +    -32    =    -34  

     -1    +    -64    =    -65  

     1    +    64    =    65  

     2    +    32    =    34  

     4    +    16    =    20  

     8    +    8    =    16    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  8  and  8  

                    h2 + 8h + 8h + 64

Step-4 : Add up the first 2 terms, pulling out like factors :

                   h • (h+8)

             Add up the last 2 terms, pulling out common factors :

                   8 • (h+8)

Step-5 : Add up the four terms of step 4 :

                   (h+8)  •  (h+8)

            Which is the desired factorization

Multiply  (h+8)  by  (h+8)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (h+8)  and the exponents are :

         1 , as  (h+8)  is the same number as  (h+8)1  

and   1 , as  (h+8)  is the same number as  (h+8)1  

The product is therefore,  (h+8)(1+1) = (h+8)2

5 • (h + 8)2

Answer 2

Answer:

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