MPT College Algebra 1 — Questions and Answers

Question 1: Simplify the expression: (x² + 5x + 6) ÷ (x + 2)

x + 3 (Correct answer)
x + 2
x + 1
x + 4

Correct answer: x + 3

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

12
7 (Correct answer)
-12
-5

Correct answer: 7

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

x = 3, -1/2 (Correct answer)
x = -3, 1/2
x = 3/2, -1
x = 1/2, -3

Correct answer: x = 3, -1/2

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?

A parabola opening up with vertex at (0, 4)
A parabola opening down with vertex at (0, -4)
A parabola opening up with vertex at (0, -4) (Correct answer)
A straight line

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

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?

1
3
5
7 (Correct answer)

Correct answer: 7

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 College Algebra 1

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

Select your answer