Question

15. The rectangular room is given by the trinomial x^2+4x-12. What are the possible dimensions of the rectangle? Use factoring. (1 point)

(x-6) and (x-2)
(x+6) and (x+2)
(x-6) and (x+2)
(x+6) and (x-2)
17. What is the factored form of the following expression? X^2+2xy-48y^2 (1 point)
a. (x+6y)(x-8y)
b. (x-6y)(x-8y)
c. (x+6y)(x+8y)
d. (x-6y)(x+8y)
18. The area of a rectangular art studio is given by the trinomial 24x^2-4x-8. What are the possible dimensions of the studio? Use factoring.
a. (3x-2) and (8x-4)
b. (3x-2) and (8x+4)
(3x-2) and (8x-4)
(3x+2) and (8x-4)

Answer 1

15. x^2 +4x - 12 = 0
We need to find square roots of this equation.
solutions are x1 = 2 and x2 = -6
using factoring we can write this equation in a form:
a* (x-x1) * (x-x2) where "a" is coefficient in front of x^2 ( in this case its 1)
therefore solution is
(x-2) and (x+6)

17. d) is the answer. To solve these kinds of questions just multiply factors and see if they match your expression.

18. again, we solve equation 24x^2 -4x -8 = 0
x1 = -1/2 and x2 = 2/3
24(x+1/2)*(x-2/3)
8(x+1/2)*(3x-2)
(8x + 4)*(3x-2)
answer is b)