# Polynomials, Quadratics, Linear Equations and Word Problems

1.Simplify -i^4: answers a.-1 b.1 c.i d.-i

2.Types of Equations

Solve by factoring: x4 - 9x2 = 0. answers a.1, -1, 3, -3 b.0, 3, -3 c.9, -9 d.3, -3

3. Two-Dimensional Coordinate System and Graphs;

Find the midpoint of the line segment with endpoints (-4, 8) and (7, 2).

a.(3/2, 5) b(-11/2, 3) c.(11/2, -3) d.(3/2, 3)

4.Introduction to Functions

Given f(x) = 3x2 + x and g(x) = 8, find f(-1) and g(2). answer

a.f(-1) = 4; g(2) = 2 b.f(-1) = 2; g(2) = 2 c.f(-1) = 2; g(2) = 8 d.f(-1) = 4; g(2) = 8

5.The length of a rectangle is 4 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 136 feet, find the length of the rectangle.

a.44 feet b.24 feet c.52 feet d. 16 feet

6.An elementary school class is selling candles to raise money to go on a field trip. The profit made by selling x candles is Profit = 1.25x - 45. How many candles must be sold to make a profit of $200? answers;

a.244 candles b.4 candles c.124 candles d.196 candles

Polynomial Division and Synthetic Division

7.Divide by X FOURTH+3XCUBIC+XSQUARED-12X-20 BY X-2

8.Find the real zeros of the polynomial function P(x) = x(x - 1)(3x + 5).

9.Find the real zeros of the polynomial function P(x) = (x + 4)(x - 6)(x + 1)3.

https://brainmass.com/math/linear-algebra/polynomials-quadratics-linear-equations-and-word-problems-31857

#### Solution Preview

1. answer is b. 1 since i^2=-1, i^4=(-1)^2=1

2. x^4-9x^2=x^2(x^2-9)=x^2*(x-3)(x+3)

So, four roots are x=0, or x=0, or x=3, or, x=-3. So, answer is b.

3. Using a formula for midpoint below

x_=(x1+x2)/2

y_=(y1+y2)/2

So, we get

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#### Solution Summary

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