Polynomials and factoring - MCQs Practice 1

Answers will be provided at the end

Practice Drill - Polynomials and Factoring

Polynomials and Factoring

(If timing, take about 12 minutes to complete the practice drill.)
Question 1 of 11
Introductory Example
(-2x² + 3x + 1) - (x² + x + 2) is equivalent to which of these expressions?
Correct Answer: C Combine the x² components, the x components, and the numerical components in order to simplify. Write out all your steps to avoid careless errors. (-2x² + 3x + 1) - (x² + x + 2) Remove the parentheses, and distribute the -1 throughout the second half of the expression: -2x² + 3x + 1 - x² - x - 2 Now, group like terms together to simplify: (-2x² - x²) + (3x - x) + (1 - 2) → -3x² + 2x - 1 This corresponds to answer choice (C).
Practice Drill - Question 1
Which of the following is equivalent to 3n(n² + 2n - 1)?
Correct Answer: A 3n(n² + 2n - 1) → Distribute the 3n → 3n³ + 6n² - 3n
Practice Drill - Question 2
x³ + 6x² + 9x Which of the following is equivalent to the above expression?
Correct Answer: C x³ + 6x² + 9x → Factor out an x → x(x² + 6x + 9) → Factor the part in parentheses → x(x + 3)(x + 3) → x(x + 3)²
Practice Drill - Question 3
x² + 12x = -36 is equivalent to which of the following?
Correct Answer: C x² + 12x = -36 → x² + 12x + 36 = 0 → (x + 6)(x + 6) = 0 → (x + 6)² = 0
Practice Drill - Question 4
Which of the following expresses the result when x³ + x is subtracted from 3x³ - 2x²?
Correct Answer: A Be careful to put this in the correct order. It should look like this: (3x³ - 2x²) - (x³ + x) → 3x³ - 2x² - x³ - x → 2x³ - 2x² - x
Practice Drill - Question 5
The expression -(x² + 2)(-x - 1) is equivalent to which of the following?
Correct Answer: C -(x² + 2)(-x - 1) → FOIL the parts within the parentheses → -(-x³ - x² - 2x - 2) → Distribute the -1 → x³ + x² + 2x + 2
Practice Drill - Question 6
(x + y²)(-x - y²) Which of the following options is an equivalent form of the expression above?
Correct Answer: B (x + y²)(-x - y²) → FOIL the expression → -x² - xy² - xy² - y⁴ → -x² - 2xy² - y⁴
Practice Drill - Question 7
5/3 + 2/(x - 3) is equivalent to which of the following, given that x ≠ 3?
Correct Answer: D Make each fraction have a common denominator and then add them together. 5/3 + 2/(x - 3) → 5(x - 3) / 3(x - 3) + 2(3) / 3(x - 3) → [5(x - 3) + 6] / 3(x - 3) → (5x - 15 + 6) / 3(x - 3) → (5x - 9) / 3(x - 3) → (5x - 9) / (3x - 9)
Fill-In Practice - Question 8
For the function f(x) = (2x - 10)², what is the value of f(13)?
Correct Answer: 256 f(x) = (2x - 10)² → f(13) = (2(13) - 10)² → f(13) = (26 - 10)² → f(13) = 16² = 256
Fill-In Practice - Question 9
If 2x/5 - 3y/10 = 0, what is the value of x/y?
Correct Answer: 3/4 or 0.75 2x/5 - 3y/10 = 0 → 2x/5 = 3y/10 → Divide both sides by y → 2x / 5y = 3/10 → Multiply both sides by 5/2 → x/y = 3/10 × 5/2 = 15/20 = 3/4
Fill-In Practice - Question 10
If 3 / (9 + 6x + x²) = 3/4, what is the value of (x + 3) if (x + 3) > 0?
Correct Answer: 2 Recognize that the denominator is the square of (x + 3), and this will be much easier to solve: 3 / (9 + 6x + x²) = 3/4 → 3 / [(x + 3)(x + 3)] = 3/4 → 3 / (x + 3)² = 3/4 → Divide both sides by 3 → 1 / (x + 3)² = 1/4 → Cross multiply to bring the values to the numerator → 4 = (x + 3)² → Take the square root of both sides: 2 = x + 3 Fortunately, we don't need to worry about imaginary solutions since the value of (x + 3) is greater than zero.