MATH 209: Basic and Intermediate Algebra

1.Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.

Write the resulting perfect square trinomial in factored form.

The resulting perfect trinomial is

2.

Show that f is not a​ one-to-one function by finding two inputs that result in the same output.

F(x) = x⁴ -3x²

3.

Evaluate the function for the given value of x

3^x   at x = 0

4.

Do the following for the given​ f(x).

​(a) Identify the vertex and axis of symmetry on the graph of  y equals ​f(x).

​(b) Graph  y equals ​f(x).

​(c) Evaluate ​f(-2​) and ​f(3​).

F(x) = x² -6

5.

The length of an office is x feet and the width is x-2 feet. Write the polynomial that represents the area. Find the area if x equals 8.

6.

Identify the greatest common factor. Then factor the expression.

4x³ -6x² +10x

7. The ______of a polynomial is the common factor with the greatest​ (integer) coefficient and highest degree.

8.  Factor as a perfect square trinomial whenever possible.

X² -10 +25

9.  Solve by using the quadratic formula.

X² -9x -52 =0

10. Multiply(x-6)(x-5)

11. Suppose that y is directly proportional to x and that  y equals 5 when x equals 3.

Complete parts ​(a) and ​(b).

a)      Find the constant of proportionality k.

b)     Use y=kx to find y when x= 9.

12. Solve and check.

x ²- 10 x + 24 = 0

13. Solve the equation  (x-7)(3x+6) =0

14.  Find the product. (4a+6) (4a -6)

15.  Use a calculator to find the common logarithm. Log 82, Log 54 and  Log 25

16. Find F^-1 (x)  and g^-1 (x)

F(x) = x/8     g(x) = 14x

17.. Find F^-1 (x)  and g^-1 (x)

F(x) = 4x-9    g(x) = (x+2)/2

18.  Add the polynomials   (3b³ + 2b² -4  )  + (2b³ - 2b +9  ) 

19.  Simplify the​ expression, if possible.

Log 10³

20.  For the functions

F(x) = x² and g(x) =  x+ 7. Find each of the following

a)      (g o f) (-3)

b)      (f o g)(2)

c)      (g o f) (x)

d)     (f o g)(x)

21. Factor the trinomial. X² + 4x + 3

22.  Find each of the following for the functions f(x) = x² -3 and g(x) =x² +3

a) (fg)(2)

b)(f-g)(x)

c) (f o g)(x)

23.  Find the domain,   P(x) = 4x -8

24.  Subtract the polynomials.  ( -3x² +5x) –(8x² +7x -2)

25.  Find the domain, F(x) = 5x/ (2x-4). ​(Type your answer in interval​ notation.)

26. Evaluate,  F(x) = 6(3^x)  at x = 0

27.  Simplify the expression.  √ 6 * 6√6

28. Factor completely a) (x² -9), b) (x² - 25), c) x² -36

29.

The braking distance D in feet required to stop a car traveling x miles per hour on​ dry, level pavement can be approximated by  D = one ninth x squared

.

(a)    ​Calculate the braking distance for  20 miles per hour and 60 miles per hour. How do your answers​ compare?

(b)   ​If the braking distance is 16​feet, estimate the speed of the car.

(c)    ​Use a calculator to solve part​ (b) numerically. Do your answers​ agree?

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30. Multiply and simplify the expression.​ a) (4​z –z) )z   b) (4z-z) (z-1)

31.

Simplify the expression. 1/ 8x +  2/3x

32.  Solve and check your answer.

x/ 4 + x/8 = 9

33.  Use f( x)= x+2  and g(x) =  x+ 3 to find each of the following

a) (f+g)(x)  b) (f-g) (x)  c) (fg)(x)  d) (f/g)(x)

34. If 3 sweaters cost  ​$29.64​, how much would 9sweaters​ cost?

35. Simplify to lowest terms  (16+5x)/ 10x – 16/10x

36.  Divide and simplify to lowest terms  (z+9)/(z-8)  divided by ( z+9)/ (z+2)

37. Divide and check ,  10x⁴/5x²

38.  A.  Write the expression 4^3/2 in radical notation.

B.  Evaluate the radical expression.

39. Factor the trinomial.  3x² + 14x+ 8

40. Evaluate , 10^{log 9}