Algebra

You must show all work
1 Subtract 3×2+7x-4 from 8×2-6x+2
Your answer should be a polynomial in standard form.
2 Multiply.
Your answer should be a monomial in standard form.
(y8)(-2y2)=
3 Expand and combine like terms.
(7b5-b2)2=
4 Plot -7-7i in the complex plane.
5 What is the greatest common factor of 15n^2, 30n^3, 45n^2?
7 What is the real part of z?
What is the imaginary part of z?
z =-302+19.3i
6 A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10% more than the number of shoppers the day before.What is the total number of shoppers that visited the mall in the first 7 days?
Round your final answer to the nearest integer.
7 Find the value of c so that (x+1)(x+1) is a factor of the polynomial p(x).
p(x)=5x^4+7x^3-2x^2-3x+c
8P(x)=3x^4-2x^3+2x^2-1
What is the remainder when P(x) is divided by (x+1)?
9 The polynomial p(x)=2x^3-x^2-25x-12 has a known factor of (x+3)
Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors.
10 Divide the polynomials.
The form of your answer should either be p(x) or p(x) + kdividedbyx+3
2x^3 -x^2-25x-12dividedbyx+3=
11 We want to find the zeros of this polynomial:
p(x)=3x^3-3x^2-18x
Plot all the zeros (x-intercepts) of the polynomial as a graph.
12 Solve the exponential equation for x.
64^7x-8= 1
13 Alyssa is an ecologist who studies the change in the fox population of the Arctic circle over time. She observed that the population loses 1dividedby8 of it’s size every 2 months. The population of foxes can be modeled by a function, P, which depends on the amount of time, t (in months).When Alyssa began the study, she observed that there were 185,000 in the Arctic circle.
Write a function that models the population of the foxes t months since the beginning of Alyssa’s study.

14 Consider the equation 11times10^5t=20 equals, 20.
14a Solve the equation for t. Express the solution as a logarithm in base -10.
t=
14b Approximate the value of t. Round your answer to the nearest thousandth.
t
15 This table defines function f:
X:    -4, -2, 0, 2, 4
f(x):   2, 1, 0, -2, -1
16
Rania solves the equation below by first squaring both sides of the equation.
-5= squareroot3x-7
What extraneous solution does Rania obtain?
x=
17
Find the following trigonometric values.
Express your answers exactly.
cos(150degrees)=
sin(150degrees)=
18
Walking on his own, the distance, D, in feet, that Roberto can cover in m minutes is given by the function D(m)=264m. When he walks on the moving sidewalk at the airport, the distance, A, in feet, that he can cover in m minutes is given by the function A(m)=440m.
Let B be the distance, in feet, that Roberto would travel on the moving sidewalk in m minutes if he were standing still.
Write a formula for B(m) in terms of D(m), and A(m)
B(m)=
Write a formula for B(m) in terms of m.
B(m)=
19 The following equation is true for all real values of n for which the expression on the left is defined, and A is a polynomial expression.
n^2+24n+144dividedbyn^2+11n-12 times  n^2+2n-3dividedby A=1
What is A?
20 Solve the exponential equation for x.
(625dividedby256)^5x-4=1
X=