Algebra II Review

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100

x(z + 3) + 1 + 3 − y; use x = 6, y = −5, and z = 2

39

200

−2(−6x − 9) − 4(x + 9)

8x-18

300

Rationalize the Imaginary Denominator (6 + 8i)/9i

(−6i + 8)/9

400

DO NOT USE YOUR CALCULATOR 111,111,111 x 111,111,111=?

12,345,678,987,654,321 :)

500

Factor each and find all zeros. One zero has been given. f (x) = 5x^3 + 4x^2 -20x -16; 2

Factors to: f (x) = (5x + 4)(x + 2)(x − 2) Zeros: {-(4/5), -2, 2}

General Functions

100

f (x) = x^2 − 3x; Find f (−8)

88

200

h(x) = 3x + 3 g(x) = −4x + 1 Find (h + g)(10)

-6

300

f (n) = 2n g(n) = −n − 4 Find ( f o g)(n) Hint: (f o g)(n)= f(g(n))

-2n-8

400

g(a) = 2a + 2 h(a) = −2a − 5 Find (g o h)(−4 + a)

-4a +8

500

Find the inverse g(x) = (1/x) -2

h(x)= (1/(x+2))

Quadratics

100

Identify the vertex and max/min value f (x) = x^2 -18x+86

vertex:(9, 5) min value: 5

200

Factor: x^2 − 7x − 18

(x − 9)(x + 2)

300

Factor: 3b^3 -5b^2 +2b

b(3b − 2)(b − 1)

400

Factor: r^3 − 7r^2 + 10r

r(r-5)(r-2)

500

Find the discriminant of each quadratic equation then state the number of real and imaginary solutions. 9n^2 − 3n − 8 = −10

−63; two imaginary solutions

Completing the square

100

Find the value of c that completes the square. x^2 + 6x + c

c=9

200

Find the value of c that completes the square x^2 + (7/13)x + c

49/676

300

Solve each function by completing the square x^2 − 12x + 11 = 0

{11,1}

400

Solve the equation by completing the square x^2 + 14x − 15 = 0

{1,-15}

500

Solve by completing the square 6x^2 − 48 = −12x

{2, −4}

Factoring

100

Solve the equation. 27 = x^(3/2)

9

200

Solve: 26 = −1 + (27x)^(3/4)

3

300

simplify (p + 4)/(p^2 +6p +8)

1/(p+2)

400

(n+3)/(n+2) ÷ ((n-1)(n+3))/((n-1)^2)

(n-1)/(n+2)

500

solve: (a − 2)/(a + 3) -1= 3/(a+2)

-19/8