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 factorizationFinal result : (x + 3) • (x - 12)