MPT College Algebra

Question 1

Simplify the expression: (x² + 5x + 6) ÷ (x + 2)

Accepted Answer

x + 3

Answer

Factor the numerator:
x² + 5x + 6 = (x + 2)(x + 3).
Now, cancel out the (x + 2) term in both the numerator and denominator:
(x + 2)(x + 3) ÷ (x + 2) = x + 3.

Question 2

Solve for x: 3x - 7 = 2x + 5

Accepted Answer

7

Answer

Subtract 2x from both sides:
3x - 7 - 2x = 2x + 5 - 2x, so x - 7 = 5.
Next, add 7 to both sides:
x = 12.

Question 3

Solve for x: 2x² - 5x - 3 = 0

Accepted Answer

x = 3, -1/2

Answer

To solve the quadratic equation 2x² - 5x - 3 = 0, use the quadratic formula:
x = [-(-5) ± √((-5)² - 4(2)(-3))] / (2(2)).
Simplifying gives:
x = [5 ± √(25 + 24)] / 4
x = [5 ± √49] / 4
x = [5 ± 7] / 4.
Thus, x = (5 + 7)/4 = 12/4 = 3, or x = (5 - 7)/4 = -2/4 = -1/2.

Question 4

Which of the following is the graph of y = x² - 4?

Accepted Answer

A parabola opening up with vertex at (0, -4)

Answer

The equation y = x² - 4 represents a parabola that opens upwards because the coefficient of x² is positive. The vertex is at (0, -4) because the equation is in the form y = x² + c, where c is the vertical shift.

Question 5

What is the value of f(x) = 2x³ - 5x² + 3 at x = 2?

Accepted Answer

7

Answer

To find f(2), substitute 2 into the function:
f(2) = 2(2)³ - 5(2)² + 3
= 2(8) - 5(4) + 3
= 16 - 20 + 3
= 7.

(MPT) UCF Math Placement Test Practice Test

(MPT) UCF Math Placement Test Practice Test

MPT College Algebra