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

(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)