ANSWER
The points are:
(32,-85)
and

EXPLANATION
The given parametric equation that defines the curve is:


We differentiate to get,


The slope of the tangent is given by;


For the slope to be 1, then we must solve the following equation for t.






When t=-2, we put -2 into the expression for x and y to get
x=4(-2)³ and y=3+40(-2)-2(-2)²
This implies that,
x=32, y=-85
Hence one point is (32,-85)
Similarly, when


Another point is

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Approximately 0.67 of a cup of sugar is needed. Let me know if this isn't right.
ANSWER
The greatest common factor is

EXPLANATION
We want to find the greatest common factor of

and

The prime factorizations are;

and

The product of the least powers of the common factors is the greatest common factor.