Solve By Factoring, and Equation of Cubic Function whose graph passes thru

[rought]

Homework Statement

I am stuck on these two pre-cal problems... can anyone help?

Solve By Factoring: 2x^3 + 2x^2 = 4x + 4

This next one I have no idea how to do

Find an equation of the cubic function whose graph passes through the points (3,0) and (1,4) and is tangent to the x-axis at the origin...

 

[Unassuming]

Homework Statement

Solve By Factoring: 2x^3 + 2x^2 = 4x + 4

Try putting all the terms on one side so that they all equal 0.

 

[rought]

alrite I think I am ok with the first problem, but I'm still stuck on the second one...

 

[Unassuming]

What can you tell from the point (3,0)?

EDIT: And what can you say since the line passes through the origin?

 

[HallsofIvy]

You need to find a, b, c, and d of y= ax³+ bx²+ cx+ d so that
a) when x= 3, y= 0
b) when x= 1, y= 4
c) when x= 0, y= 0 and y'= 3ax²+ 2b²+ c= 0.

Putting those values in the equation gives you four linear equations for a,b,c, and d.

 

[rought]

Alright, I think i have it...

It is x^2 because there is a tangent on the x-axis at (0,0), and the other zero is (x-3)

Through a bit of trial and error I have come to: -2x^2(x-3) and I am pretty sure that works just fine.


Thanks again everyone who helped you guys are great!