Solve Plynomial (Grade 11 Principals Math)?

Question

x^3 - (13x^2)/4 + x = -3

I am totally confused, I get it down to 4x^3 - 52x^2 + 4x +12 = 0 and I don't even know if that is right.

Answer 1

Clear the denominator to get
4x³ -13x² +4x+12 = 0.
(Your 52 should be 13)
Now if a/b is any rational root of this equation
a must divide 12 and b must divide 4.
Testing all the possibilities, we find that 2 is a root,
so x-2 is a factor.
The quotient is 4x² - 5x -6. You can get this by
long division or synthetic division.
But 4x²-5x-6 = (x-2)(4x+3)
So the left side of your equation becomes
(x-2)(x-2)(4x+3) = 0,
and the roots are x = 2, x = 2 and x = -3/4.
The equation has a double root at x = 2, so it
is tangent to the x-axis at that point.

Answer 2

x³ - (13/4)x² + x = -3
rearrange so all terms on on side set equal to 0
x³ - (13/4)x² + x + 3 = 0
multiply through by 4
4x³ - 13x² + 4x + 12 = 0
if this confuses you, it gets trickier
did you get a term to factor this by, like (x + 2)
finding this solution requires factoring with a term
if you were not given one, you need to find one
set this problem up in long division form and try different factors like x+2 or x-3 and divde out until even
set this problem up, try it, then take it to the teacher or teacher's assistant or any math teacher and ask for help
they will see you have tried to solve it and be more willing to help then just approcahing them and saying you're totally confused.
great answer, steiner. I appreciate knowing the root approach. thank you as well.