rectangular box has a volume of 6x^2- 600. If the width of the box is 6, select all of the expressions that represent the box's length and height.
A)x + 50
B)x-50
C)x + 25
D)X-4
E)x + 10
F)x-10
To find the length and height of the box, we need to factor the given volume expression and look for two factors that multiply to give 6x^2 - 600.
The prime factorization of 6x^2 - 600 is 6(x+20)(x-10).
Since the width of the box is 6, we are looking for two factors that multiply to give 6(x+20)(x-10) when multiplied by 6.
Setting 6x+20 = 6 and x-10 = 6, we find that x=2 and x=16.
Therefore, the length and height of the box are 2 + 20 = 22 and 16 - 10 = 6, respectively.
Out of the given expressions, the correct answers are:
A) x + 50 (length)
D) x-4 (height)