College Algebra 9th txtbk

SECTION B–3 Parametric Equations A-23
B-2 Exercises
In Problems 1–4, find A and B so that the right side is equal to the
left. After cross-multiplying to produce a polynomial equation,
solve each problem two ways (see Explore-Discuss 1). First,
equate the coefficients of both sides to determine a linear system
for A and B and solve this system. Second, solve for A and B by
evaluating both sides for selected values of x.
1.
2.
3.
4.
In Problems 5–10, find A, B, C, and D, so that the right side is
equal to the left.
5.
7.
8.
7x 14
(x 4)(x 3) A
x 4 B
x 3
9x 21
(x 5)(x 3) A
x 5 B
x 3
17x 1
(2x 3)(3x 1) A
2x 3 B
3x 1
x 11
(3x 2)(2x 1) A
3x 2 B
2x 1
3x 2 7x 1
x(x 1) 2 A x B
x 1
x 2 6x 11
6.
(x 1)(x 2) A
2 x 1 B
x 2 C
(x 2) 2
3x 2 x
(x 2)(x 2 3) A
x 2 Bx C
x 2 3
5x 2 9x 19
(x 4)(x 2 5) A
x 4 Bx C
x 2 5
9. 2x2 4x 1
(x 2 x 1) 2 Ax B
x 2 x 1
C
(x 1) 2
Cx D
(x 2 x 1) 2
10.
In Problems 11–30, decompose into partial fractions.
x 22
x 21
3x 13
11. 12. 13.
x 2 2x 8 x 2 2x 15 6x 2 x 12
11x 11 x 2 12x 18 5x 2 36x 48
14. 15. 16.
6x 2 7x 3 x 3 6x 2 9x x(x 4) 2
5x 2 3x 6 6x 2 15x 16 2x 3 7x 5
17. 18. 19.
x 3 2x 2 3x x 3 3x 2 4x x 4 4x 2 4
5x 2 7x 18
x 3 7x 2 17x 17
20. 21.
x 4 6x 2 9
x 2 5x 6
x 3 x 2 13x 11
22.
x 2 2x 15
4x 2 5x 9
4x 2 8x 1
23. 24.
x 3 6x 9
x 3 x 6
x 2 16x 18
5x 2 18x 1
25. 26.
x 3 2x 2 15x 36 x 3 x 2 8x 12
27.
3x 3 3x 2 10x 4
(x 2 x 3) 2 Ax B
x 2 x 3
x 2 x 7
x 4 5x 3 9x 2 8x 4
2x 3 12x 2 20x 10
28.
x 4 7x 3 17x 2 21x 18
4x 5 12x 4 x 3 7x 2 4x 2
29.
4x 4 4x 3 5x 2 5x 2
30. 6x5 13x 4 x 3 8x 2 2x
6x 4 7x 3 x 2 x 1
Cx D
(x 2 x 3) 2
B-3 Parametric Equations
Z Parametric Equations and Plane Curves
Z Projectile Motion
Z Parametric Equations and Plane Curves
Consider the two equations
x t 1
y t 2 2t
6 t 6
(1)