1.

Solve long division methodX³+8x²-9x+30

Answer»

Step-by-step explanation:

The first term is,  x^2  its coefficient is  1 .

The middle term is,  +9X  its coefficient is  9 .

The last term, "the CONSTANT", is  +18 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18 

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   9 .

3   +   6   =   9   That's it

Step-3 : Rewrite the polynomial SPLITTING the middle term using the two factors found in step 2 above,  3  and  6 

                     x2 + 3x + 6x + 18

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

                    x • (x+3)

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

                    6 • (x+3)

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

                    (x+6)  •  (x+3)

             Which is the desired factorization.

X³+8x²-9x+30= (x-1)(x+6)(x+3)

x= 1 or x= -6 x= -3


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