Question 1Easier
Which of the following expressions is equivalent to ?
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Answer: A —
.
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Polynomial expressions and factoring — ACT practice questions
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Practice 58 Polynomial expressions and factoring questions in the app
What this topic is
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.
Sample questions
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Question 2Easier
Which of the following expressions is equivalent to ?
Show answer
Answer: A —
Expanding gives . Combining the middle terms yields .
Question 3Mid
How many distinct real zeros does have?
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Answer: D — 4
Treat the expression as a quadratic in : . Thus, the distinct real zeros are and 2, for a total of 4.
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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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