Question

factorize (x^2+8x)(x^2+8x+5)-14

Answer 1

Given (x^2 + 8x)(x^2 + 8x + 5) - 14 

         = x^2  * x^2 + x^2 * 8x + x^2 * 5 + 8 * x * x^2 + 8x * 8x + 8x * 5 - 14

         = x^4 + 16x^3 + 5x^2 + 64x^2 + 40x - 14

         = x^4 + 16x^3 + 69x^2  + 40x - 14

         = (x+1)(x^3 + 15x^2 + 54x - 14)

         = (x+1)(x+7)(x^2+8x-2).


Hope this helps!

Answer 2

 x2-8x-84=0 

Two solutions were found :

 x = 14 x = -6

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x2-8x-84 

The first term is,  x2  its coefficient is  1 .
The middle term is,  -8x  its coefficient is  -8 .
The last term, "the constant", is  -84 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -84 = -84 

Step-2 : Find two factors of  -84  whose sum equals the coefficient of the middle term, which is   -8 .

     -84   +   1   =   -83     -42   +   2   =   -40     -28   +   3   =   -25     -21   +   4   =   -17     -14   +   6   =   -8   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  6