A cubic function of the y=ax^3+bx^2+cx+d

yields the following table:

a=-5

b=4

c=-1

d=0

Step-by-step explanation:

The given cubic equation is of the form;

When x=0 and y=0, we get:

when x=1 and y=-2, we get:

When x=2 and y=-26, we get:

When x=3 and y=-54, we get:

We need to solve the system:

From the top equation:

Put this expression into equation 2 and 3

also

Now we solve the system:

subtract the top equation from the down one to get:

This implies that:

and

207/8 is the right

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb