C 957 | C957 Exam 3: Applied Algebra Updated and
Latest Questions and Correct Answers with
Rationale - WGU
1. Simplify the following expression: (4x^2 - 3x + 5) + (2x^2 + 7x - 8).
A. 8x^2 + 4x - 3
B. 6x^2 + 10x + 13
C. 6x^2 + 4x - 3
D. 2x^2 + 4x - 3
Correct Answer: C
Explanation: To simplify the sum of two polynomials, you must combine the like terms
together. Adding the squared terms 4x^2 and 2x^2 results in 6x^2. Combining the linear
terms -3x and 7x gives a result of 4x. Finally, adding the constants 5 and -8 equals -3. The
resulting simplified expression is 6x^2 + 4x - 3.
2. Which of the following is the factored form of x^2 - 11x + 24?
A. (x - 8)(x - 3)
B. (x - 12)(x - 2)
C. (x + 8)(x + 3)
D. (x - 6)(x - 4)
Correct Answer: A
Explanation: Factoring a trinomial involves finding two numbers that multiply to the
constant term and add to the middle coefficient. In this case, we need factors of 24 that sum
to -11. The numbers -8 and -3 multiply to 24 and add to -11. Therefore, the binomial factors
are (x - 8) and (x - 3). Other combinations like -12 and -2 do not sum to -11.
3. Factor the expression 9x^2 - 49 completely.
A. (3x - 7)(3x - 7)
B. (9x - 1)(x + 49)
C. (3x + 7)^2
D. (3x - 7)(3x + 7)
Correct Answer: D
Explanation: The expression 9x^2 - 49 is a difference of two squares. This follows the
algebraic pattern a^2 - b^2, which factors into (a - b)(a + b). Here, a is the square root of
,9x^2, which is 3x, and b is the square root of 49, which is 7. Thus, the factored form is (3x -
7)(3x + 7). Squaring a single binomial would produce a middle term, which is absent here.
4. What are the solutions to the quadratic equation x^2 - 5x - 14 = 0?
A. x = 7, x = -2
B. x = -7, x = 2
C. x = 14, x = -1
D. x = 5, x = -14
Correct Answer: A
Explanation: To solve by factoring, set the equation to zero and find factors of -14 that sum
to -5. The factors are -7 and 2 because their product is -14 and their sum is -5. Setting the
factors (x - 7)(x + 2) equal to zero gives the solutions. Solving x - 7 = 0 yields x = 7, and
solving x + 2 = 0 yields x = -2. Therefore, the correct solutions are 7 and -2.
5. What value of ‘c’ makes the expression x^2 + 12x + c a perfect square trinomial?
A. 12
B. 36
C. 144
D. 6
Correct Answer: B
Explanation: To complete the square for x^2 + bx, you must add the square of half of b. In
this problem, the coefficient b is 12. Half of 12 is 6, and squaring 6 results in 36. Thus, c
must be 36 to create the perfect square (x + 6)^2. Choosing 144 or 12 would not result in a
binomial squared.
6. Use the quadratic formula to find the roots of x^2 - 4x + 1 = 0.
A. x = 4 ± √12
B. x = 2 ± √3
C. x = -2 ± √3
D. x = 2 ± √5
Correct Answer: B
Explanation: Using the quadratic formula, x = [-b ± √(b^2 - 4ac)] / 2a, we substitute a=1,
b=-4, and c=1. This gives x = [4 ± √(16 - 4)] / 2, which simplifies to [4 ± √12] / 2. Since √12
is 2√3, the expression becomes [4 ± 2√3] / 2. Dividing both terms by 2 results in the final
answer of 2 ± √3. Option B is incorrect because it is not fully simplified.
, 7. Identify the vertex of the quadratic function f(x) = (x + 5)^2 - 3.
A. (-5, -3)
B. (-5, 3)
C. (5, -3)
D. (5, 3)
Correct Answer: A
Explanation: The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k. In
this form, the vertex is the point located at (h, k). For the given equation (x + 5)^2 - 3, h is -
5 and k is -3. Therefore, the vertex of the parabola is exactly (-5, -3). Incorrect options
confuse the signs of the horizontal or vertical shifts.
8. Which way does the parabola f(x) = -2x^2 + 4x - 1 open, and why?
A. Upward, because the leading coefficient is negative.
B. Upward, because the constant term is negative.
C. Downward, because the leading coefficient is negative.
D. Downward, because the linear term is positive.
Correct Answer: C
Explanation: The direction in which a parabola opens is determined by the sign of the
leading coefficient ‘a’. In the standard form ax^2 + bx + c, if a is positive, the parabola opens
upward. Here, the leading coefficient is -2, which is a negative number. This means the
graph must open downward toward negative infinity. The signs of the other terms do not
affect the direction of opening.
9. Solve the equation x^2 = 81 using the square root property.
A. x = 9
B. x = -9
C. x = ±9
D. x = 81
Correct Answer: C
Explanation: The square root property states that if x^2 = k, then x is equal to the positive
or negative square root of k. Since 81 is a perfect square, its roots are 9 and -9. Taking the
square root of both sides requires including both the plus and minus signs. Therefore, x = 9
and x = -9 are both valid solutions. Only providing one sign would lead to an incomplete
solution set.
Latest Questions and Correct Answers with
Rationale - WGU
1. Simplify the following expression: (4x^2 - 3x + 5) + (2x^2 + 7x - 8).
A. 8x^2 + 4x - 3
B. 6x^2 + 10x + 13
C. 6x^2 + 4x - 3
D. 2x^2 + 4x - 3
Correct Answer: C
Explanation: To simplify the sum of two polynomials, you must combine the like terms
together. Adding the squared terms 4x^2 and 2x^2 results in 6x^2. Combining the linear
terms -3x and 7x gives a result of 4x. Finally, adding the constants 5 and -8 equals -3. The
resulting simplified expression is 6x^2 + 4x - 3.
2. Which of the following is the factored form of x^2 - 11x + 24?
A. (x - 8)(x - 3)
B. (x - 12)(x - 2)
C. (x + 8)(x + 3)
D. (x - 6)(x - 4)
Correct Answer: A
Explanation: Factoring a trinomial involves finding two numbers that multiply to the
constant term and add to the middle coefficient. In this case, we need factors of 24 that sum
to -11. The numbers -8 and -3 multiply to 24 and add to -11. Therefore, the binomial factors
are (x - 8) and (x - 3). Other combinations like -12 and -2 do not sum to -11.
3. Factor the expression 9x^2 - 49 completely.
A. (3x - 7)(3x - 7)
B. (9x - 1)(x + 49)
C. (3x + 7)^2
D. (3x - 7)(3x + 7)
Correct Answer: D
Explanation: The expression 9x^2 - 49 is a difference of two squares. This follows the
algebraic pattern a^2 - b^2, which factors into (a - b)(a + b). Here, a is the square root of
,9x^2, which is 3x, and b is the square root of 49, which is 7. Thus, the factored form is (3x -
7)(3x + 7). Squaring a single binomial would produce a middle term, which is absent here.
4. What are the solutions to the quadratic equation x^2 - 5x - 14 = 0?
A. x = 7, x = -2
B. x = -7, x = 2
C. x = 14, x = -1
D. x = 5, x = -14
Correct Answer: A
Explanation: To solve by factoring, set the equation to zero and find factors of -14 that sum
to -5. The factors are -7 and 2 because their product is -14 and their sum is -5. Setting the
factors (x - 7)(x + 2) equal to zero gives the solutions. Solving x - 7 = 0 yields x = 7, and
solving x + 2 = 0 yields x = -2. Therefore, the correct solutions are 7 and -2.
5. What value of ‘c’ makes the expression x^2 + 12x + c a perfect square trinomial?
A. 12
B. 36
C. 144
D. 6
Correct Answer: B
Explanation: To complete the square for x^2 + bx, you must add the square of half of b. In
this problem, the coefficient b is 12. Half of 12 is 6, and squaring 6 results in 36. Thus, c
must be 36 to create the perfect square (x + 6)^2. Choosing 144 or 12 would not result in a
binomial squared.
6. Use the quadratic formula to find the roots of x^2 - 4x + 1 = 0.
A. x = 4 ± √12
B. x = 2 ± √3
C. x = -2 ± √3
D. x = 2 ± √5
Correct Answer: B
Explanation: Using the quadratic formula, x = [-b ± √(b^2 - 4ac)] / 2a, we substitute a=1,
b=-4, and c=1. This gives x = [4 ± √(16 - 4)] / 2, which simplifies to [4 ± √12] / 2. Since √12
is 2√3, the expression becomes [4 ± 2√3] / 2. Dividing both terms by 2 results in the final
answer of 2 ± √3. Option B is incorrect because it is not fully simplified.
, 7. Identify the vertex of the quadratic function f(x) = (x + 5)^2 - 3.
A. (-5, -3)
B. (-5, 3)
C. (5, -3)
D. (5, 3)
Correct Answer: A
Explanation: The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k. In
this form, the vertex is the point located at (h, k). For the given equation (x + 5)^2 - 3, h is -
5 and k is -3. Therefore, the vertex of the parabola is exactly (-5, -3). Incorrect options
confuse the signs of the horizontal or vertical shifts.
8. Which way does the parabola f(x) = -2x^2 + 4x - 1 open, and why?
A. Upward, because the leading coefficient is negative.
B. Upward, because the constant term is negative.
C. Downward, because the leading coefficient is negative.
D. Downward, because the linear term is positive.
Correct Answer: C
Explanation: The direction in which a parabola opens is determined by the sign of the
leading coefficient ‘a’. In the standard form ax^2 + bx + c, if a is positive, the parabola opens
upward. Here, the leading coefficient is -2, which is a negative number. This means the
graph must open downward toward negative infinity. The signs of the other terms do not
affect the direction of opening.
9. Solve the equation x^2 = 81 using the square root property.
A. x = 9
B. x = -9
C. x = ±9
D. x = 81
Correct Answer: C
Explanation: The square root property states that if x^2 = k, then x is equal to the positive
or negative square root of k. Since 81 is a perfect square, its roots are 9 and -9. Taking the
square root of both sides requires including both the plus and minus signs. Therefore, x = 9
and x = -9 are both valid solutions. Only providing one sign would lead to an incomplete
solution set.
