Answer:
Step-by-step explanation:
A) 3x²c² + 5xc² - 2c²
Factor c² from all terms in the expression.
c²(3x² + 5x - 2)
Factor 3x² + 5x - 2
c²(3x-1)(x+2)
B) x² + 6x + 9
x² + 3x + 3x + 9
Factor common terms.
x(x+3)+3(x+3)
Take x+3 common.
(x+3)(x+3)
C) x² - 9
x² -3²
Apply formula : a² - b² = (a+b)(a-b)
(x+3)(x-3)
If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides and
, and a height of x.
So, the volume will be given by the product of the dimensions, i.e.
The derivative of this function is
and it equals zero if and only if
If we evaluate the volume function at these points, we have
So, the maximum volume is given if you cut a square with side length