Algebra polynomials
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Please help in completing the following pre-exam practice questions and show all work at to how you got the final answer.
1. (5x2 - 4xy + 4y2) - (2x2 - xy + 2y2)
2. 3x2y (2x2 - xy2 + 3y3)
3. (3x + 2)(5x - 4)
4. (2x - 7)2
5. (2a + 3b)(2a - 3b)
6. (12x4 - 16x3+ 8x) / (4x)
7. (3.2 x 106)(2.4 x 10-4)
Factor completely or state that the polynomial is prime.
8. 12x2 - 16x + 4
9. x2 - 256
10. x2 +10x - 24
11. 25y2 + 10y + 1
12. x2 - 5x - 24
13. 10x2 + 7x - 12
Perform the indicated operation.
14. x / (x + 2) + 2 / x
15. 3 / (x - 2) - 2 / (x + 5)
16. 2 / (x + 1) + 3 / (x2 - 1)
Solve the equations, express complex solutions in a + ib form.
17. (y - 3)2 = 7
18. x2 + 6x + 9 = 0
19. 2x2 - x - 6 = 0
20. x2 - 25 = 0
21. x2 - 5x - 6 = 0
22. x2 = 4x - 2
23. x2 + 3x + 1 = 0
24. x2 - 3x + 3 = 0
25. (x - 3)2 = -10
26. x2 + 2x + 3 = 0
27. Find the vertex of the parabola y = 2x2 - 8x + 7.
28. Find the y-intercept for the parabola y = x2 - 3x + 10.
29. Find the x-intercepts for the parabola y = -2x2 + 10x - 5.
30. Find the vertex of the parabola y = x2 + 16.
31. If f(x) = x2 + 2x + 1, find f(a).
32. If g(x) = x - x2 / 2, find g(0.1).
33. If f(x) = x2 + 3x + 4, find f(i) where i = (-1)1/2.
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Solution Summary
This shows how to find x-intercepts and vertex of a parabola, values of a function at given points, solutions to quadratic equations (including complex/imaginary solutions), factors of a polynomial (or that it is prime), and simplified polynomials.
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Algebra Practice Questions
Please help in completing the following pre-exam practice questions and show all work at to how you got the final answer.
1. (5x2 - 4xy + 4y2) - (2x2 - xy + 2y2)
Removing the brackets, we get 5x2 - 4xy + 4y2 - 2x2+ xy - 2y2
Clubbing the like terms we get
5x2- 2x2 - 4xy + xy + 4y2- 2y2=3x2-3xy+2y2
2. 3x2y (2x2 - xy2 + 3y3)
Multiplying each term in the bracket with 3x2y, we get
6x4y-3x3y3+9x2y4
The formula used in the above problem is am x an=am+n
3. (3x + 2)(5x - 4)
Removing the brackets and multiplying term by term, we get
(3x)(5x) - 4(3x) + 2(5x) - 8 = 15x2 - 2x - 8
4. (2x - 7)2
Using the formula for (a-b)2=a2+b2-2ab, we can write (2x-7)2=(2x)2+72-2(2x)7=4x2+49-28x
5. (2a + 3b)(2a - 3b)
Using the formula (a+b)(a-b)=a2-b2, we get
(2a + 3b)(2a - 3b)=(2a)2-(3b)2=4a2-9b2
6. (12x4 - 16x3+ 8x) / (4x)
Removing the brackets and dividing each term by 4x, we get
(12x4 - 16x3+ 8x) / (4x)= 12x4/ (4x)- 16x3/ (4x)+ 8x/ (4x)=3x3-4x2+2
The formula used in the above problem is am / an=am-n
7. (3.2 x 106)(2.4 x 10-4) =(3.2 x 106)(2.4 x 10-4)= (3.2 x 2.4)x106-4=7.68x102
Factor completely or state that the polynomial is prime.
8. 12x2 - 16x + 4
Observe that all the coefficients are multiples of ...
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