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MTH 219T Wk 5 – Final Exam

Question 1

10 Points
Solve $3 x^{2} + 4 x - 4 = 0$ .

$x = \frac{2}{3} o r x = - 2$

$x = - \frac{2}{3} o r x = 2$

$x = - \frac{2}{3} o r x = - 2$

$x = \frac{2}{3} o r x = 2$
Question 2

10 Points
Solve $\frac{x^{2} + 8 x + 16}{x + 4} = \frac{- 1}{x + 2}$ .

$x = - 3$

$x = 3, - 2$

$x = - 3, 2$

$x = 3$
Question 3

10 Points
Find the vertex of the parabola $y = 4 x^{2} - 16 x + 4$ .

$(- 2, - 12)$

$(- 2, 12)$

$(2, 12)$

$(2, - 12)$
Question 4

10 Points
Factor the expression $2 x^{2} + 15 x + 28$ .

$(x - 4) (2 x - 7)$

$(x + 4) (2 x + 7)$

$(x - 4) (2 x + 7)$

$(x + 4) (2 x - 7)$
Question 5

10 Points
Factor the expression $15 x^{3} - 12 x^{2} - 30 x + 24$ .

$(3 x^{2} + 6) (5 x - 4)$

$(3 x^{2} - 6) (5 x - 4)$

$(3 x^{2} + 6) (5 x + 4)$

$(3 x^{2} - 6) (5 x + 4)$
Question 6

10 Points
Identify the polynomial that matches the sum or difference of cubes.

$8 x^{3} - 16$

$x^{3} + 9$

$x^{3} + 121$

$125 x^{3} - 216$
Question 7

10 Points
Simplify $\frac{6 - x}{x^{2} - 8 x + 12}$ .

$\frac{1}{x - 2}$

$\frac{- 1}{x + 2}$

$\frac{1}{x + 2}$

$\frac{- 1}{x - 2}$
Question 8

10 Points
The length of a rectangle is 6 meters more than its width. The area of the rectangle is 114 square meters. Which of the following quadratic equations represents the area of the rectangle? Suppose x is the width of the rectangle.

$x^{2} + 6 x + 114 = 0$

$x^{2} + 6 x - 114 = 0$

$x^{2} - 6 x + 114 = 0$

$x^{2} - 6 x - 114 = 0$
Question 9

10 Points
Solve $x^{2} + 8 x - 20 = 0$ .

$x = 2 o r x = - 10$

$x = 5 o r x = 3$

$x = 5 o r x = - 3$

$x = - 2 o r x = 10$
Question 10

10 Points
Factor the expression $5 x^{3} + 30 x^{2} - 45 x$ .

$- 5 x (x^{2} - 6 x + 9)$

$- 5 (x^{2} + 6 x - 9)$

$5 x (x^{2} + 6 x - 9)$

$5 (x^{2} + 6 x - 9)$
Question 11

10 Points
Which of the following is a rational expression?

$\frac{x^{2} - 2 x - 5}{x^{3} + 5 x}$

$3 x + x^{\frac{5}{3}}$

$4^{x} + x^{4}$

$\sqrt{\frac{x^{2} + 1}{3 x}}$
Question 12

10 Points
Factor the expression $5 x^{3} + 30 x^{2} + 45 x$ completely.

$5 x (x + 3) (x + 3)$

$x (x + 3) (x - 3)$

$5 x (x - 3) (x + 3)$

$x (x - 3) (x - 3)$
Question 13

10 Points
Simplify $5 x - 15 \div \frac{x^{2} - 9}{x + 2}$ .

$\frac{5 (x + 3)}{x + 10}$

$\frac{5 x - 10}{x + 3}$

$\frac{5 x + 10}{x + 3}$

$\frac{5 (x - 3)}{x + 10}$
Question 14

10 Points
Factor the trinomial $x^{2} - 11 x + 30$ .

$(x - 5) (x + 6)$

$(x + 5) (x + 6)$

$(x + 5) (x - 6)$

$(x - 5) (x - 6)$
Question 15

10 Points
Add $\frac{6 x}{x^{2} - 3 x + 2} + \frac{5}{x^{2} - 5 x + 6}$ .

$\frac{6 x^{2} - 23 x - 5}{(x - 1) (x - 2)^{2} (x - 3)}$

$\frac{6 x^{2} - 13 x - 5}{(x - 1) (x - 2) (x - 3)}$

$\frac{6 x + 5}{(x - 1) (x - 2) (x - 3)}$

$\frac{6 x + 5}{(x - 1) (x - 2)^{2} (x - 3)}$
Question 16

10 Points
Reduce the complex fraction $\frac{5 y + \frac{1}{x - 5}}{\frac{3 x + 1}{3}}$ .

$\frac{15 x y + 75 y + 3}{3 x^{2} + 14 x - 5}$

$\frac{15 x y + 75 y}{3 x^{2} - 5}$

$\frac{15 x y - 75 y + 3}{3 x^{2} - 14 x - 5}$

$\frac{15 x y + 3}{3 x^{2} + 5}$
Question 17

10 Points
Find the value of m to complete the square: $x^{2} + 7 x + m = 31 + m$ .

49

7

$\frac{7}{4}$

$\frac{49}{4}$
Question 18

10 Points
Simplify $\frac{x - 5}{6} \cdot \frac{18}{x^{2} - 10 x + 25}$ .

$\frac{x - 5}{3}$

$\frac{x + 5}{3}$

$\frac{3}{x + 5}$

$\frac{3}{x - 5}$
Question 19

10 Points
Solve $2 x^{2} + 5 x - 3 = 0$ by completing the square.

$x = - 3 o r x = \frac{1}{2}$

$x = 3 o r x = - \frac{1}{2}$

$x = \frac{3}{2} o r x = - 1$

$x = - \frac{3}{2} o r x = - 1$
Question 20

10 Points
Subtract $\frac{1}{3 x + 3} - \frac{5}{3 (x^{2} + 2 x + 1)}$ .

$\frac{x - 4}{3 (x + 1)^{2}}$

$\frac{x - 4}{(x + 1)}$

$\frac{x - 5}{(x + 1)^{2}}$

$\frac{x - 5}{3 (x + 1)}$

MTH 219T Wk 5 – Final Exam

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