How do you find the degree, leading term, the leading coefficient, the constant term and the end behavior of #P(x)=(x-1)(x-2)(x-3)(x-4)#?

Question

Ariana Alvarez · Accepted Answer

Degree=4, leading coefficient =1
behavior:-
as x tends toward +ve or -ve infinite the value of polynomial tends towards infinite.

As the polynomial states for the max power of x x should be multiplied with x from each bracket which gives us #x^4# . so the degree becomes 4. When the we multiply from each bracket we get 1 as leading coefficient as all brackets have 1 as coefficient of x . had they been a, b ,c ,d the leading coefficient would have been #a*b*c*d#. nd as we increase the value of x towards positive or negative the lhs keeps on getting greater so the behavior would be x tends to -ve infinite when x increase on -ve axis and x tends to +ve infinite when x increase on +ve axis.

Lincoln Anderson · Answer

undefined The degree of $ P(x) = (x-1)(x-2)(x-3)(x-4) $ is 4.
The leading term is $ x^4 $.
The leading coefficient is 1.
The constant term is -24.
The end behavior:
As $ x $ approaches positive or negative infinity, $ P(x) $ approaches positive infinity because the leading term dominates the behavior.