Question

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)`?

Answer 1

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

Explanation:

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.