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Beurre
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An example is x^3 + x^2 + ax -72
Factor is x+3
F(-3) doesn't equal zero and I am out of other ideas. Help? :/
Factor is x+3
F(-3) doesn't equal zero and I am out of other ideas. Help? :/
Beurre said:An example is x^3 + x^2 + ax -72
Factor is x+3
F(-3) doesn't equal zero and I am out of other ideas. Help? :/
Hello Beurre. Welcome to PF !Beurre said:An example is x^3 + x^2 + ax -72
Factor is x+3
F(-3) doesn't equal zero and I am out of other ideas. Help? :/
You could do long hand polynomial division of the cubic equation by the known factor in order to end up with a quadratic equation and a remainder that will be some linear function of a, which you can then solve for a, or as already suggested subsitute x = -3 into the equation and solve for a.Beurre said:An example is x^3 + x^2 + ax -72
Factor is x+3
In order to find the unknown in a cubic equation, you will need to use the factor theorem. This theorem states that if a polynomial equation has a factor, then the value of that factor will be a root of the equation. So, if you are given a factor, you can plug it into the equation and solve for the unknown.
No, the quadratic formula can only be used to solve for the unknown in a quadratic equation, not a cubic equation. To solve for the unknown in a cubic equation, you will need to use the factor theorem or use other methods such as synthetic division or the rational root theorem.
A factor is a number or expression that divides evenly into a polynomial equation, while a root is a value that makes the equation equal to zero. In other words, a factor is a solution to the equation, while a root is a specific value that satisfies the equation.
Yes, it is possible to have more than one factor in a cubic equation. In fact, the fundamental theorem of algebra states that a polynomial equation of degree n has exactly n complex roots, which means it can have multiple factors.
No, in order to use the factor theorem, you will need to know at least one factor and its corresponding root. This means you will need to know three factors in order to solve for the unknown in a cubic equation using the factor theorem.