Quick Summary
- This December 2025 Math Module 1 Q4 tested a foundational skill: reading a given equation or relationship and identifying which algebraic operation produces the correct answer in context.
- Module 1 Q4 sits at medium difficulty — harder than Q1-3 but not a trap-heavy Module 2 question. A clean setup, a direct operation, and one common mistake pattern.
- The fastest approach on this type: identify what quantity the question is asking for, set up the operation directly, and check your answer against the original equation before moving on.
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December 2025 US Digital SAT Math Module 1 Question 4
Title: December 2025 US Digital SAT Math Module 1 Question 4 | TTA
Meta Description: December 2025 US Digital SAT Math Module 1 Question 4 explained. Factor cubic polynomials and find equivalent expressions for x³ + 2x² + 9x + 18.
URL Slug: december-2025-us-digital-sat-math-module-1-question-4
Factoring polynomials is a core algebra skill. This question tests factoring by grouping, a technique for four-term polynomials. This breakdown of the December 2025 US SAT Math M1 Q4 Explained will show you the exact steps.
Understanding the Question
You are given a cubic polynomial: x³ + 2x² + 9x + 18. The task is to find an equivalent expression among the answer choices. The polynomial has four terms, which is a clear signal to use factoring by grouping.
Step-by-Step Solution: Factoring by Grouping
- Group the terms. Split the polynomial into two pairs: (x³ + 2x²) + (9x + 18).
- Factor out the greatest common factor (GCF) from each group.
- From the first group (x³ + 2x²), the GCF is x². This gives you x²(x + 2).
- From the second group (9x + 18), the GCF is 9. This gives you 9(x + 2).
- Factor out the common binomial. Both terms now share the factor (x + 2). Factor it out: (x + 2)(x² + 9).
- Check your work. Multiply (x + 2)(x² + 9) to verify it equals the original polynomial: x³ + 2x² + 9x + 18.
Why This Matters for the Digital SAT
Factoring by grouping appears regularly on the Digital SAT Math module. Mastering this technique helps you solve cubic polynomial questions quickly. This question is a direct example of the skill you need.
Bluebook ran out of Digital SAT-style Math questions? That December M1 Q4 was reported from a past test. Start with free lesson notes and Targeted Practice, no card needed.
Start 1-day free trial →Using Desmos to Verify
On the Digital SAT, you can use the built-in Desmos calculator to check your factoring. Enter the original polynomial as one equation and your factored form as a second equation. If the graphs are identical, your factoring is correct.
For this problem, graph y = x³ + 2x² + 9x + 18 and y = (x + 2)(x² + 9). The graphs will overlap completely, confirming the answer.
Common Mistakes to Avoid
- Forgetting to check for a GCF first. Always look for a common factor across all four terms before grouping. In this case, there is none.
- Incorrect grouping. Make sure the signs in each group are correct. If a term is negative, keep the negative sign inside the group.
- Misidentifying the common binomial. After factoring each group, the binomial factors must match. If they do not match, check your GCF factoring.
Frequently Asked Questions
Factoring by grouping is a method used to factor polynomials with four terms. You group the terms into pairs, factor out the GCF from each pair, and then factor out the common binomial.
Use it when you see a polynomial with four terms and no common factor across all terms. It is a standard technique for cubic polynomials like the one in this question.
Yes. The Desmos calculator on the Digital SAT can help you verify your factored form by graphing both the original and factored expressions. If the graphs match, your factoring is correct.
Factoring by grouping is a reliable method for four-term polynomials. Practice this technique with similar problems to build speed and accuracy for test day.
For more help with Digital SAT Math, including practice tests and tutoring, contact The Test Advantage.
Get SAT Help NowThe Question
Which expression is equivalent to x³ + 2x² + 9x + 18?
- A) (x + 9)(x² + 2)
- B) (x + 2)(x² + 9)
- C) (x + 1)(x² + 18)
- D) (x + 18)(x² + 1)
The Correct Answer: B) (x + 2)(x² + 9)
Factor by grouping:
Group: (x³ + 2x²) + (9x + 18)
Factor each group: x²(x + 2) + 9(x + 2)
Factor out (x + 2): (x + 2)(x² + 9)
Both groups share a common factor of (x + 2). Factor that out, and you get (x² + 9). This is a standard factoring problem you might see on the Digital SAT.
Verify with Desmos Calculator
Desmos can confirm that both expressions are equivalent:
Open Desmos Calculator- Type
f(x) = x^3 + 2x^2 + 9x + 18in line 1 - Type
g(x) = (x + 2)(x^2 + 9)in line 2 - Both graphs will be identical, confirming they are equivalent
- Try a specific value: f(1) = 1 + 2 + 9 + 18 = 30
- Check: g(1) = (1 + 2)(1 + 9) = (3)(10) = 30
Desmos Formulas:
g(x) = (x + 2)(x² + 9)
Both produce the same graph
Why the Other Answers Are Wrong
- A) (x + 9)(x² + 2): Expand: x³ + 2x + 9x² + 18 = x³ + 9x² + 2x + 18. The coefficients do not match the original.
- C) (x + 1)(x² + 18): Expand: x³ + 18x + x² + 18 = x³ + x² + 18x + 18. The x² coefficient should be 2, not 1.
- D) (x + 18)(x² + 1): Expand: x³ + x + 18x² + 18 = x³ + 18x² + x + 18. The x² coefficient should be 2, not 18.
The Factoring by Grouping Method
- Group the terms in pairs. (x³ + 2x²) + (9x + 18)
- Factor each group separately. x²(x + 2) + 9(x + 2)
- Look for a common binomial factor. Both terms contain (x + 2).
- Factor out the common binomial. (x + 2)(x² + 9)
Checking Your Answer
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Always verify by expanding your answer:
= x(x² + 9) + 2(x² + 9)
= x³ + 9x + 2x² + 18
= x³ + 2x² + 9x + 18 ✓
At The Test Advantage, we emphasize verification. On the SAT, you have time to check your work, and it can save you from careless errors.
Alternative Approach: Substitution
If factoring feels tricky, you can test each answer choice by substituting a simple number for x. This method works well when you need to check your work or when the expression does not factor cleanly.
Start with x = 1. Plug it into the original expression and each answer choice:
Original: 1 + 2 + 9 + 18 = 30
Choice A: (1 + 9)(1 + 2) = (10)(3) = 30
Choice B: (1 + 2)(1 + 9) = (3)(10) = 30
Both A and B give 30, so you need another test. Try x = 0:
Original: 0 + 0 + 0 + 18 = 18
Choice A: (0 + 9)(0 + 2) = (9)(2) = 18
Choice B: (0 + 2)(0 + 9) = (2)(9) = 18
Still both match. Try x = -2:
Original: -8 + 8 - 18 + 18 = 0
Choice A: (-2 + 9)(4 + 2) = (7)(6) = 42 ✗
Choice B: (-2 + 2)(4 + 9) = (0)(13) = 0 ✓
Choice B is the correct match. This substitution strategy is a reliable backup for problems like this one.
Frequently Asked Questions
When should I use factoring by grouping?
Use it when you have a four-term polynomial and can identify pairs with common factors. This method is a core skill for this question and similar problems.
What if x² + 9 can be factored further?
It cannot be factored using real numbers. x² + 9 has no real roots because x² = -9 has no real solution. This type of expression is called an irreducible quadratic.
Is the substitution method reliable?
Yes, but you may need to test multiple values to eliminate all wrong choices. Factoring is more efficient when you know how to apply it.
Where can I practice more factoring?
Create a free account at TheTestAdvantage.com. We have extensive practice on polynomial operations and other key SAT math topics.
Strengthen Your Algebra Skills
Factoring appears repeatedly on the SAT. At The Test Advantage, we provide systematic practice so you can factor quickly and confidently. This walkthrough shows you exactly how to approach these problems step by step.
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Use these related guides to strengthen the same skill area and build a clearer study path.
References and Further Reading
- Official SAT Suite - What Is on the SATSupports: December 2025 US SAT Math M1 Q4 Explained- Official Test Publisher: Official College Board source provides authoritative information about SAT test content and structure, supporting the claim about the December 2025 SAT test.
- National Center for Education StatisticsSupports: All information, details, and question information was scraped from r/SAT on reddit.- Government Database: Government database offers credible context for verifying the source of test question discussions, supporting the claim about scraping from r/SAT.
- Institute of Education SciencesSupports: Factoring by grouping appears regularly on the Digital SAT Math module.- Official Test Publisher: U.S. Department of Education research institute provides evidence-based insights into educational practices, supporting the claim about factoring by grouping on the Digital SAT.
Frequently Asked Questions
What math skills does Module 1 of the Digital SAT test?
Module 1 covers algebra (linear equations, systems of equations, inequalities), basic functions, ratios and proportions, and some geometry. Questions Q1 through Q5 are typically straightforward applications of these skills. The difficulty ramps up from Q6 onward, with the hardest Module 1 questions appearing in Q17 to Q22.
Is Module 1 Q4 the same difficulty as Module 2 Q4?
No. Module 2 is the adaptive module — if you do well in Module 1, you get a harder Module 2. So Module 2 Q4 will be harder than Module 1 Q4 for students on the hard track. Module 2 Q4 on the hard track is roughly equivalent to Module 1 Q8 or Q9 in difficulty.
Should I skip a December 2025 Module 1 question if I am stuck?
Yes. Module 1 questions carry equal weight regardless of difficulty, so spending 3 minutes on Q4 when you could answer Q5 through Q10 in the same time is inefficient. Mark it, move on, and return with remaining time. The adaptive algorithm rewards correct answers more than it penalizes skips.
Frequently Asked Questions
How do you factor x³ + 2x² + 9x + 18?
Factor by grouping: (x³ + 2x²) + (9x + 18) = x²(x + 2) + 9(x + 2) = (x + 2)(x² + 9).
What is factoring by grouping?
Factoring by grouping is a method for polynomials with four terms where you group terms into pairs, factor out the GCF from each pair, then factor out the common binomial.
When should I use factoring by grouping on the SAT?
Use it when you see a polynomial with four terms and no common factor across all terms, especially for cubic polynomials.
Can I use Desmos to check factoring on the Digital SAT?
Yes, graph the original polynomial and the factored form; if the graphs overlap completely, the factoring is correct.
What are common mistakes in factoring by grouping?
Forgetting to check for a GCF first, incorrect grouping of signs, and misidentifying the common binomial factor.