Question

Graph the polynomial function. Factor first if the expression is not in factored form.

f(x) = x^3 + 7x^2=4x-12

Answer #1

Graph the polynomial function. Factor first if the expression is not in factored form.

Perhaps the 2^{nd} = sign is a mistake. Then, we have
f(x) = x^{3} + 7x^{2}+4x-12. Now, as per the
rational roots theorem, the roots of f(x) are likely to be of the
form p/q where p is a factor of -12 and q is a factor of 1. The
factors of -12 are ± 1,2,3,4,6,12 and the factors of 1 are ± 1.
Further, f(1) = 1+7+4-12 = 0. Hence 1 is a root of f(x) so that
(x-1) is a factor of f(x). Then f(x) = (x-1)x^{2} +8(x-1)x
+12(x-1) = (x-1)(x^{2} +8x+12) =
**(x-1)(x+6)(x-2).**

A grapf off(x) is attached. It may be observed that the graph crosses the X-Axis at x = -6,-2 and 1.

write the polynomial equation f(x) in factored form with leading
coefficient -2, and zeros -1(double root), 1 (single root), and 3
(single root).
A) write f(x) in factored form
B) What is its degree?
C) what is its y-intercept
D) sketch the graph showing the zeros and y-intercept

Use synthetic division to factor the polynomial: f(x) =
2x4 + 7x3 + x2 − 7x − 3

(1 point) Find the degree 3 Taylor polynomial T3(x) centered
at a=4 of the function f(x)=(7x−20)4/3.
T3(x)=
? True False Cannot be determined The function f(x)=(7x−20)4/3
equals its third degree Taylor polynomial T3(x) centered at a=4.
Hint: Graph both of them. If it looks like they are equal, then do
the algebra.

1.Determine all the zeros and their multiplicities of the
polynomial function f(x) = x 5 − 6x 3 + 4x 2 + 8x − 16
2. Find all the zeros of the function f(x) = x 5 − 4x 4 + x 3 −
4x 2 − 12x + 48 given that −2i and 4 are some of the zeros.

f(x) = (sin x)2(cos
x)5
a) Find the first derivative of your function in fully factored
form
b) Find the critical numbers over the domain
c) Find the exact slope of the tangent to your function at x=
4
d) Find the exact equation of the tangent to your function at x=
4 in slope y intercept form

Given that a polynomial function g has g(1)=-96, and has
x-intercepts at x = -3 (multiplicity 3), x=-1 (m.1), and 2 (m. 2),
sketch the graph of the function, then write a equation for g(x)
(can leave function in factored form) and describe its end
behavior.

Find the degree 3 Taylor polynomial T3(x) of function
f(x)=(7x−5)^3/2 at a=2. T3(x)=

For the function f(x) = ln(4x), find the 3rd order Taylor
Polynomial centered at x = 2.

(1 point) Find the degree 3 Taylor polynomial T3(x) of
function
f(x)=(7x+67)^(5/4)
at a=2
T3(x)=?

Let
f(x) be polynomial function in field F[x].
f’(x) be the derivative of f(x).
Given the greatest common factor (f(x), f’(x))=1.
And (x-a)|f(x). Show that (x-a)^2 can not divide f(x).

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