Question

The area of a rectangle painiting is given by the trinomial x^2-9x-36. what are the possible dimensions of the painting ? use factoring

Answer 1

(x + 3) • (x - 12)

The first term is,  x2  its coefficient is  1 .
The middle term is,  -9x  its coefficient is  -9 .
The last term, "the constant", is  -36 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -36 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -9 .

     -36   +   1   =   -35     -18   +   2   =   -16     -12   +   3   =   -9   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3 
                     x2 - 12x + 3x - 36

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-12)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-12)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-12)
             Which is the desired factorization

Final result : (x + 3) • (x - 12)