GED Math Practice Test: Polynomials and Quadratic Equations
- Polynomials, Factoring and Quadratic Equations
- 10 questions
- 15 minutes
These 10 questions cover the polynomial and quadratic skills on the GED Mathematical Reasoning test: combining like terms, multiplying binomials, factoring and solving quadratic equations. The quadratic formula is on the GED formula sheet, so practice plugging values in carefully, especially negative signs.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
Which expression is equivalent to (3x2 − 5x + 2) − (x2 + 4x − 7)?
Correct answer: B
Subtracting a polynomial changes the sign of every term in it: 3x2 − x2 = 2x2, −5x − 4x = −9x and 2 + 7 = 9. The choice 2x2 − x − 5 comes from adding the second polynomial instead of subtracting it.
-
Question 2
Which expression is equivalent to (2x − 3)(x + 5)?
Correct answer: C
Multiply each term: 2x · x = 2x2, 2x · 5 = 10x, −3 · x = −3x and −3 · 5 = −15. The middle terms combine to 7x. Writing only 2x2 − 15 skips the two middle products.
-
Question 3
Which is the factored form of x2 − x − 12?
Correct answer: A
You need two numbers whose product is −12 and whose sum is −1: −4 and 3. The pair 4 and −3 also multiplies to −12, but it adds to +1, which would give x2 + x − 12.
-
Question 4
What are the solutions of x2 − 7x + 10 = 0?
Correct answer: D
The equation factors as (x − 2)(x − 5) = 0, so x = 2 or x = 5. Check: 4 − 14 + 10 = 0. The choice −2 or −5 comes from taking the numbers inside the factors without solving each factor for x.
-
Question 5
Use the quadratic formula to solve 2x2 + 3x − 4 = 0. What is the positive solution, rounded to the nearest hundredth?
Correct answer: B
With a = 2, b = 3 and c = −4, the discriminant is 9 − 4(2)(−4) = 41, so x = (−3 + √41) ÷ 4 ≈ 0.85. The choice 1.70 comes from dividing by 2 instead of by 2a = 4.
-
Question 6
Which expression shows 6x3 − 9x2 + 15x with its greatest common factor factored out?
Correct answer: A
The greatest common factor of 6, 9 and 15 is 3, and every term contains at least one x, so the GCF is 3x. Dividing each term by 3x gives 2x2 − 3x + 5. The choice with 6x fails because 9 and 15 are not multiples of 6.
-
Question 7
The length of a rectangular patio is 3 feet more than its width. The area of the patio is 70 square feet. What is the width of the patio?
Correct answer: B
If the width is w, then w(w + 3) = 70, so w2 + 3w − 70 = 0 and (w + 10)(w − 7) = 0. A width cannot be negative, so w = 7 ft. The 10 ft choice is the length, not the width.
-
Question 8
If f(x) = x2 − 3x + 2, what is f(−4)?
Correct answer: D
Substitute −4 for every x: (−4)2 − 3(−4) + 2 = 16 + 12 + 2 = 30. The choice −2 comes from treating (−4)2 as −16.
-
Question 9
Which expression is equivalent to 9x2 − 25?
Correct answer: C
9x2 − 25 is a difference of squares: (3x)2 − 52 = (3x − 5)(3x + 5). Expanding (3x − 5)2 gives 9x2 − 30x + 25, which has a middle term.
-
Question 10
A ball is kicked straight up from the ground. Its height in feet after t seconds is h = −16t2 + 64t. After how many seconds does the ball land on the ground?
Correct answer: C
The ball is on the ground when h = 0: −16t(t − 4) = 0, so t = 0 (the kick) or t = 4. At 2 seconds the ball is at its highest point, not on the ground.
Questions you leave blank are not counted as wrong.
More Math tests
MathGED Math Practice Test: Statistics and ProbabilityStatistics and Probability10 questions15 min MathGED Math Practice TestMathematical Reasoning12 questions18 minMathGED Math Practice Test 2: Algebra, Geometry and DataAlgebra, Geometry and Data15 questions22 minMathGED Math Practice Test: Ratios, Percents and GeometryQuantitative Problem Solving: Ratios, Percents and Geometry15 questions25 minMathGED Math Practice Test: Area, Volume and Surface AreaArea, Volume and Surface Area10 questions15 minMathGED Math Practice Test: Linear Functions, Slope and GraphsLinear Functions, Slope and Graphs10 questions15 minMathGED Math Practice Test: Fractions, Exponents and Scientific NotationNumber Sense: Fractions, Exponents and Scientific Notation10 questions15 min