Final answer:
The given equation cannot be factored using rational roots theorem or any other factorization methods. The degree of the equation is 3 and the leading coefficient is 5. The end behavior of the graph approaches positive infinity as x approaches negative infinity, and approaches negative infinity as x approaches positive infinity.
Step-by-step explanation:
The given equation is y = -x + 5x³ - x² - 21x + 18.
The factored form of the equation can be found by finding the roots of the equation. However, it seems that the equation cannot be factored using rational roots theorem or any other factorization methods. Therefore, the equation cannot be factored.
The degree of the equation is the highest power of x in the equation, which is 3.
The leading coefficient of the equation is the coefficient of the term with the highest power of x, which is 5.
The end behavior of the graph can be determined by looking at the leading term. Since the leading term is 5x³, the graph approaches positive infinity as x approaches negative infinity, and approaches negative infinity as x approaches positive infinity.
The multiplicity of the roots of the equation can be determined by factoring the derivative of the equation and finding the roots. However, since the equation cannot be factored, we cannot determine the multiplicity of the roots.
The y-intercept of the graph can be found by substituting x = 0 into the equation, which gives y = 18. Therefore, the y-intercept is 18.
Unfortunately, without the ability to factor the equation, we cannot find specific graph numbers such as relative maxima and minima, points of inflection, or concavity.