The amount of possible solutions to a polynomial will be based on the degree of the polynomial. Ex. X^3 will have three possible solutions.

Rule of thumb

Standard Form​:

​f(x) = ax³ + bx² + cx + d

Cubic Functions Standard form. ​

Some text here about the topic of discussion

​There are three ways to solve cubic equations: Two are kind of special cases and one is the standard way.

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​Two special cases

Common factor:

• In this type there would be no constant term.

• Example 1 Solve for x: x^3 + 5x^2 – 14x = 0

• Solution x(x^2 + 5x – 14) = 0

• x(x + 7)(x – 2) = 0

• x = 0, x = 2, x = –7

Second Special case

Grouping:​

With this type, we must have all four terms of the cubic expression. We then pair terms with a common factor and see if a common bracket emerges.

• ​​Solve for x: x^3 + 2x^2 – 9x – 18 = 0

• (x3 + 2x2 ) – (9x + 18) = 0​

• ​x^2 (x + 2) – 9(x + 2) = 0

• ​(x + 2)(x2 – 9) = 0

• ​(x + 2)(x – 3)(x + 3) = 0

• ​x = –2, x = 3, x = –3