**Polynomial Analysis** In this exercise, we are tasked with analyzing the polynomial function: \[ p(x) = 14 + 5x^4 - 7x^5 \] ### Tasks: **(A) The leading term of the polynomial** The leading term of a polynomial is the term with the highest power of \( x \). For the polynomial \( p(x) = 14 + 5x^4 - 7x^5 \), the leading term is: \[ -7x^5 \] **(B) The limit of \( p(x) \) as \( x \) approaches \(\infty\)** The limit as \( x \) approaches infinity determines the behavior of the polynomial for very large values of \( x \). The leading term, \( -7x^5 \), dominates the behavior. As \( x \rightarrow \infty \), \( -7x^5 \rightarrow -\infty \). **(C) The limit of \( p(x) \) as \( x \) approaches \(-\infty\)** Similarly, for very large negative values of \( x \), the leading term also dominates the behavior of the polynomial. As \( x \rightarrow -\infty \), \( (-7x^5) \) also approaches \(-\infty\). ### Conclusion: - The polynomial's leading term is \( -7x^5 \). - As \( x \) approaches \(\infty\), \( p(x) \) approaches \(-\infty\). - As \( x \) approaches \(-\infty\), \( p(x) \) also approaches \(-\infty\).

Q: Use polynomial division to express the following rational functions as a quotient plus a rational…

A: We can find the answer as below.

Q: A polynomial function P(x) is given by 5x^3+bx^2+cx+d and has zeros at the points (0,0) and (2,0).…

A: We can find value of b as follows

Q: how do i find a high order polynomial equation that  passes through the points (190,145), (160,180),…

A: how do i find a high order polynomial equation that  passes through the points (190,145), (160,180),…

Q: Let p(x)=2⋅x^3+5−x^5+5⋅x^2−2⋅x^4+4⋅x . Determine for the polynomial p(x) its: degree, fifth degree…

A: The degree of a polynomial is the highest power of the variable x in the polynomial. In the given…

Q: Let p(x)=−5⋅x^3−2⋅x^5−4⋅x^2+3⋅x^4 . Determine for the polynomial p(x) its degree, cubic coefficient,…

A: The degree of a polynomial is the highest power of the variable x in the polynomial. In the given…

Q: use synthetic division to prove that the number k is lower bound for the real zeros of the function…

A:

Q: Determine a rational expression that could have the simplified form q(x) =(x-8)/x restrictions x ≠…

A: Given,            The simplified form qx=x-8x restrictions x ≠ 0,+8,-8.To find : Determine a…

Q: Select the function the expression the product of (f * g)(x) = f(x)= -4x and g(x)= 2x-1 divided by…

A:

Q: Find and simplify f(x)*f(g) f(x)=5x^2-9x-2 / 5x^2-8x-4   and g(x)=x^2+7x+12 / 5x^2+16x+3

A: