How do you factor this completely?
6x-x^3-x^2
6x-x^3-x^2
= -x(x^2 + x - 6)
= -x(x+3)(x-2)
Factor 6X-X^3-X^2 completely.
Step1. Arrange exponents in decreasing order: -x^3-x^2+6x.
Step2.-X(X^2+X-6)
Step3. -X(X-2)(X+3).
The equation in step2 is not completely
factored, because the trinomial can be
factored into 2 binomials (step 3).
To factor the expression completely, we can start by looking for any common factors among the terms. In this case, there isn't a common factor other than the variable "x." So, let's factor out an "x" from each term:
x(6 - x^2 - x)
Next, let's focus on factoring the trinomial expression inside the parentheses, which is "6 - x^2 - x." Since it has three terms, we'll try to factor it by grouping.
Step 1: Rearrange the expression in descending order of the exponent:
x(-x^2 - x + 6)
Step 2: Now, look for two numbers that multiply to give the product of the coefficient of the quadratic term (-1) and the constant term (6) and add up to give the coefficient of the linear term (-1). In this case, the numbers are -3 and 2 because (-3)(2) = -6 and -3 + 2 = -1.
Step 3: Rewrite the linear term (-x) by splitting it using the numbers found in step 2:
x(-x^2 - 3x + 2x + 6)
Step 4: Group the terms in pairs:
x[(-x^2 - 3x) + (2x + 6)]
Step 5: Factor out the greatest common factor from each group:
x[-x(x + 3) + 2(x + 3)]
Step 6: Combine the factored terms:
x(x + 3)(-x + 2)
Therefore, the completely factored form of the expression 6x - x^3 - x^2 is x(x + 3)(-x + 2).