# cubics

• Feb 9th 2008, 06:42 PM
chaneliman
cubics
how guys, i haven't done cubics for quite some time.
how would you go about finding the x intercepts of a cubic such as x^3 - 3x -2? Also how would u move such a cubic in the negative direction of the x axis.
• Feb 9th 2008, 06:51 PM
Soroban
Hello, chaneliman!

Quote:

How would you find the x-intercepts of: .$\displaystyle y \:=\:x^3 - 3x -2$
You might note that $\displaystyle x = 2$ is a zero of the polynomial.

Using long division to factor: .$\displaystyle x^3-3x-2 \:=\:(x-2)(x^2+2x+1) \;=\;(x-2)(x+1)^2$

The $\displaystyle x$-interecepts are: .$\displaystyle 2\text{ and }-1$

Quote:

How would u move such a cubic in the negative direction of the x axis?
To move it $\displaystyle a$ units to the left, replace $\displaystyle x$ with $\displaystyle (x+a)$.

• Feb 9th 2008, 06:55 PM
mr fantastic
Quote:

Originally Posted by chaneliman
how guys, i haven't done cubics for quite some time.
how would you go about finding the x intercepts of a cubic such as x^3 - 3x -2? Also how would u move such a cubic in the negative direction of the x axis.

Solve $\displaystyle x^3 - 3x - 2 = 0$.

f(x) ---> f(x + a) where a > 0 will move the graph of y = f(x) a units to the left.

Oh ..... now you want to konw how to solve $\displaystyle x^3 - 3x - 2 = 0$ ......

Trial and error. x = -1 seems to work. So x + 1 is a factor. So now you can factorise: $\displaystyle (x + 1)(x^2 - .... -2)$.

Or you could do a clever grouping: $\displaystyle x^3 - 3x - 2 = (x^3 + 2x^2 + x) - (2x^2 + 4x + 2) = x(x^2 + 2x + 1) - 2(x^2 + 2x + 1) = .......$.

Oh yes ..... In advance - you're welcome ........ (Thinking)
• Feb 9th 2008, 06:58 PM
chaneliman
i understand everything except "You might note that is a zero of the polynomial."
• Feb 9th 2008, 07:00 PM
Jhevon
Quote:

Originally Posted by chaneliman
i understand everything except "You might note that is a zero of the polynomial."

this is from the rational roots theorem (look it up). to find the possible rational roots here (that is, the x-values that cause the function to give a value of zero) we try the factors of 2. so we try +/- 1, and +/- 2. and it turns out that x = 2 and x = -1 work