jacksonbobby5 said:Homework Statement
I need help trying to factor a trinomial. It has been a while, and I can't remember how to factor a trinomial with x^3. Please help.
Sample problem...
X^3 - 2X^2 + 1
Thanks
Homework Equations
The Attempt at a Solution
Not sure where to start, I would think I would factor out an X
Maybe: X^2 (1X - 2 + 1)
?
This is incorrect. If you simplify the expression in parentheses, you get x - 1. If you then multiply x^2 and x -1, you get x^3 - x^2, which is different from what you started with.jacksonbobby5 said:Homework Statement
I need help trying to factor a trinomial. It has been a while, and I can't remember how to factor a trinomial with x^3. Please help.
Sample problem...
X^3 - 2X^2 + 1
Thanks
Homework Equations
The Attempt at a Solution
Not sure where to start, I would think I would factor out an X
Maybe: X^2 (1X - 2 + 1)
A factor trinomial with x3 is a polynomial with three terms that includes an x-squared term, an x-term, and a constant term, and the leading coefficient of the x-squared term is not equal to 1. The term with the highest degree, in this case x3, is also referred to as the leading term.
To factor a trinomial with x3, first check if there is a common factor among all three terms. If there is, factor it out. Then, use the grouping method to factor the remaining terms. Split the x3 term into two terms, such as x2 and x, and the constant term into two terms, such as -2 and 5. Group the terms with common factors, and factor out the greatest common factor from each group. Finally, use the distributive property to simplify and combine like terms, resulting in two binomial factors.
Sure, consider the trinomial 2x3 - 5x2 - 12x. First, factor out the greatest common factor of 2x, resulting in 2x(x2 - 5x - 6). Then, group the remaining terms as (x2 - 6x) + (-5x - 6). Factor out the greatest common factor from each group, resulting in x(x - 6) - 3(5x + 6). Finally, use the distributive property to simplify and combine like terms, resulting in (x - 3)(2x - 2). Therefore, the factored form of the original trinomial is 2x(x - 3)(x - 2).
The purpose of factoring a trinomial with x3 is to simplify the expression and make it easier to work with. It also allows us to find the roots or solutions of the trinomial, which are the values of x that make the trinomial equal to 0. Factoring can also help us to identify patterns and relationships between the terms in the trinomial.
Yes, there are two special cases to consider when factoring a trinomial with x3. The first case is when the constant term is equal to 0. In this case, we can factor out an x from each term, resulting in x(x2 - 5x - 12). The second case is when the trinomial is a perfect square trinomial, meaning the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms. In this case, we can use the formula (a + b)2 = a2 + 2ab + b2, where a and b are the square roots of the first and last terms, respectively. For example, x2 + 6x + 9 can be factored as (x + 3)2.