Question 1
Which of the following expressions is equivalent to ?
- A
- B
- C
- D
Show answer
Answer: A —
.
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Polynomial expressions and factoring — ACT practice questions
Polynomial expressions and factoring on the ACT Mathematics test covers expanding products, rewriting polynomials in equivalent factored form, and finding zeros of a polynomial that factors cleanly. A student has to expand a squared binomial, factor a quadratic trinomial, and count the distinct real zeros of a higher-degree polynomial, often after treating it as a quadratic in a squared variable. Items usually ask which expression is equivalent to a given polynomial or how many distinct real zeros it has. Answer choices look like near-miss expansions and factorizations that differ by a sign, a middle term, or a repeated root.
- Section: Mathematics 45 questions on the paper
- 58 practice questions in the app
Sample questions
Question 2
Which of the following expressions is equivalent to ?
- A
- B
- C
- D
Show answer
Answer: A —
Expanding gives . Combining the middle terms yields .
Question 3
How many distinct real zeros does have?
- A0
- B2
- C3
- D4
Show answer
Answer: D — 4
Treat the expression as a quadratic in : . Thus, the distinct real zeros are and 2, for a total of 4.
Practice 58 Polynomial expressions and factoring questions in the app
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Quadratic equations
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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