1) Simplify (x+1)42) Solve for x: 2x2 = 3x + 14

Solution:(x+1)(x+1)(x+1)(x+1)Solution: Change to 2x2 – 3x – 14 = 0

(x2 + 2x + 1)(x2 + 2x +1) Factor into (2x - 7)(x + 2) = 0

x4 + 4x3 +6x2 + 4x +1 Set each factor equal to zero:

2x – 7 = 0 or x + 2 = 0

x = 7/2 or -2

3) Graph y = x3 +2x2 – 4x – 84) Solve for x: 4x2 – x + 1 = 0

(Label the x intercepts)

Solution:This is not factorable so you

Solution:Enter the equation intoshould use the quadratic formula.

“y1 =” and graph. x interceptsx =

are at x = -2, 2x =

x =

5) If (1 – 2i) is a solution for x2 + bx + c = 0, where b and c are real numbers, what is the value of b?

Solution: Since 1 - 2i is a root, so is 1 + 2i. The sum of the two roots is the opposite of b. By adding 1 – 2i to 1 + 2i to get 2, the value of b is -2.

6) If y = x2 + 8x + 3 is written in the form of y = a(x – h)2 + k, what is the value of k?

Solution: By completing the square you can write the equation in the vertex form.

Move 3 to the other side of the equation: y – 3 = x2 + 8x

Take half of the linear coefficient and add

its square to both sides of the equation:y – 3 + 16 = x2 + 8x + 16

Write as a binomial that is squared:y + 13 = (x + 4)2

Move the 13 back to the other side:y = (x + 4)2 – 13

Therefore k = -13

7) Divide 3x3 – 2x2 + 4x – 5 by x – 3.8) A circle of radius 6 contains the center of

(3, -2), what is the equation of the circle?

Solution:Use synthetic division since

the divisor is linear.Solution: Since the circle has the formula of

______(x-h)2 + (y-k)2 = r2 where the center is (h, k)

3 )3 -2 4 -5and the radius is r.

__ 9 21 75(x – 3)2 + (y + 1)2 = 36

3 7 25)70

= 3x2 + 7x + 25 +

9) A box, with one side given as x, has the volume of V = 40x – 26x2 + 4x3. What is the

smallest positive value of x to generate the largest volume?

Solution:Graph V on a x-y axis and see the third degree equation crossing at x = 0, 2.5, and 4. The maximum value of the volume will occur when y = 18 and x = 1.

Answer x = 1

10) Given the function f(x) = x3 – 11x2 + 24x what is the solution for f(x) > 0 in terms of x?

Solution: This function factors into x(x2 – 11x +24) = 0

x(x - 8)(x - 3) = 0

x = 0, x = 8, x = 3

Looking at the graph has f(x) positive if x is between 0 and 3 or x > 8.

Answer: 0 < x < 3 or x > 8