SOLUTION: I need to pass the real test. So can someone please tell me if i got these questions wrong or right. it will really be a BIG help. Questions 1-3 Simplify the expression: 1

Question 490731: I need to pass the real test. So can someone please tell me if i got these questions wrong or right.
it will really be a BIG help.

Questions 1-3 Simplify the expression:
1. x2-4x+4(x2+2x-5) Answer: 5x2+12x-20
2. 5x2+4x-6(3x2-2) Answer: -13x2+4x-12
3. x2(4x-x+6) Answer: 3x2+6
Multiply the binomials:
4. (a+b)(a-b) Answer: a2-b2
Questions Multiply 5-9:
5. (4a+x)(3a-x) Answer: 12a2+7ax-x2
6. h2(5h+4) Answer: 5h3+4h2
7. (x+3)2 Answer: x2+9
8. (d-5)2 Answer: d2-25
9. (2x2)(x+4)(x-4) Answer: 2x4-16
11. To graphically solve the quadratic equation x2+3x-10=5. Answer: Use the quadratic formula, letting a=1, b=3, and c=-15.
12. If the garden box has dimensions x by x feet and an area in square feet equal to the perimeter in feet, what is the value for x that satisfies the requirements? (Hint: The box is square.) Answer: There is not enough information in the problem.
13. Given three consecutive integers with a sum of four times the second number, write an algebraic equation for this situation. Answer: 3n+3=4n
14. Factor the trinomial b2-b-6. Answer: (b+3)(b-2)
15. Factor the binomial x2-64. Answer: (x-8)(x+8)
16. Factor the binomial 9a2-16. Answer: (3a-4)(3a+4)
17. Factor the equation x2=x+20. Answer: (x+5)(x+4)
18. Solve the equation x2+5x-4=0 using the quadratic formula. Answer: x=.702 and -5.702
19.Solve the equation 3m2+6m=3 using the quadratic formula. Answer: x=2.5 and -14.5
Questions 20-21 write the value of the discriminant of each equation, decide how many different real-number roots the equation has, and determine how many points the parabola will interact with the x-axis. Do not solve the equation.
20. x2+7x+9=0 Answer: Discriminant is 13,indicating there are two real roots, with the parabola intersecting the x-axis at two points.
21. 2x2+5x+7=0 Answer: Discriminant is -31, indicating there are no real roots, with the parabola not intersecting the x-axis at all. Thanks :C
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Questions 1-3 Simplify the expression:
1. x2-4x+4(x2+2x-5) Answer: 5x2+12x-20
That can't be right. Are you supposed to multiply?
--------------
2. 5x2+4x-6(3x2-2) Answer: -13x2+4x-12
Same as #1
-----------
3. x2(4x-x+6) Answer: 3x2+6
Same as #1
------------
Multiply the binomials:
4. (a+b)(a-b) Answer: a2-b2
= , correct.
----------------
Questions Multiply 5-9:
5. (4a+x)(3a-x) Answer: 12a2+7ax-x2
It's -4ax and + 3ax
-->
-----------------
6. h2(5h+4) Answer: 5h3+4h2 Correct
7. (x+3)2 Answer: x2+9

-------------
8. (d-5)2 Answer: d2-25
Do it like #7
----------------
9. (2x2)(x+4)(x-4) Answer: 2x4-16
No.
= AMP Parsing Error of [(2x^2*(x^2 - 16)]: Invalid expression. Closing bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 187. .
----------------
11. To graphically solve the quadratic equation x2+3x-10=5. Answer: Use the quadratic formula, letting a=1, b=3, and c=-15.
12. If the garden box has dimensions x by x feet and an area in square feet equal to the perimeter in feet, what is the value for x that satisfies the requirements? (Hint: The box is square.) Answer: There is not enough information in the problem.
13. Given three consecutive integers with a sum of four times the second number, write an algebraic equation for this situation. Answer: 3n+3=4n
-------------------
14. Factor the trinomial b2-b-6. Answer: (b+3)(b-2)
If you multiply your answer, you'll see the sign of b is wrong.
---------------------
15. Factor the binomial x2-64. Answer: (x-8)(x+8) Correct
-----------------
16. Factor the binomial 9a2-16. Answer: (3a-4)(3a+4) Correct
-----------------
17. Factor the equation x2=x+20. Answer: (x+5)(x+4)
Equations are solved, not factored ????
----------------
18. Solve the equation x2+5x-4=0 using the quadratic formula. Answer: x=.702 and -5.702
Solve by factoring.

(x-4)*(x-1) = 0
x = 1, 4
----------
19.Solve the equation 3m2+6m=3 using the quadratic formula. Answer: x=2.5 and -14.5
3m2+6m=3

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:

m = x
--------------

--------------------------------------
Questions 20-21 write the value of the discriminant of each equation, decide how many different real-number roots the equation has, and determine how many points the parabola will interact with the x-axis. Do not solve the equation.
20. x2+7x+9=0 Answer: Discriminant is 13,indicating there are two real roots, with the parabola intersecting the x-axis at two points.
Correct.
-----------------
21. 2x2+5x+7=0 Answer: Discriminant is -31, indicating there are no real roots, with the parabola not intersecting the x-axis at all.
Correct.
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