Question 1Easier
Which of the following expressions is equivalent to ?
Show answer
Answer: A —
.
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Mathematics
Polynomial expressions and factoring — ACT practice questions
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What this topic is
Recognizing patterns speeds up Polynomial expressions and factoring.
Squaring a binomial produces three terms, so x plus three, squared, equals x squared plus six x plus nine, not x squared plus nine, a mistake that drops the middle term. Factoring reverses multiplication, and grouping handles trinomials with a leading coefficient other than one. Some polynomials of degree four behave like quadratics in x squared, so substituting a new letter for x squared turns them into familiar problems.
ACT Mathematics asks which expression is equivalent to a given one or how many real zeros a polynomial has, and expanding a factored choice is a reliable way to confirm it.
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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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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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