Question

solve the equation x^2 - 3x^2-22x+24=0


do you use a graph?

Answer 1

x^2 - 3x^2-22x+24=0
is a quadratic with two like terms.
Would you like to double check for typos?

Answer 2

sorry its x^3-3x....

Answer 3

Have you done factoring of polynomials?

Answer 4

I notice that the sum of all the coefficients is zero.
Do you know how that would help?

Answer 5

i factored by grouping and got x^2(x-3) -2(11x-12) = 0
so now do i set the equal to zero?

Answer 6

Grouping has to be done in such a way as to have a common factor.
With cubics, the usual strategy is to find an obvious factor, then reduce the cubic to a quadratic by synthetic (or long) division.

The first factor is to check for
(x-1). If all the coefficients add to zero, then x-1 is a factor.
Here: 1-3-22+24=0 so (x-1) is a factor. So you can proceed to do the division and factor the quadratic, if possible.

If the first step fails, the next factor to look is (x+1).
To check, add coefficients but reverse the sign of the coefficient when the power is odd.
Here <b>-</b>1-3<b>+</b>22x+24=42, so (x+1) is not a factor.

If nothing works, try applying the rational root theorem, and Descartes' rule of signs.

Answer 7

thanks for the help. i don't think i learned all of that yet and i don't understand.