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Expressions and Polynomials on the GED Math Test

An expression is algebra with no equals sign. On the GED that means four jobs: turning a sentence into an expression, evaluating one when you are told what the letter equals, tidying one by combining like terms, and multiplying or factoring polynomials. There is nothing to solve; the question is whether you can rewrite what you were given without changing what it is worth, and every wrong answer on offer is a rewrite that changed the value somewhere.

Updated September 21, 2026 · Lessons by Coach Crissy

Questions per set
10
Skills covered
7
Score-report category
Algebraic problem solving with expressions and equations · 30% of the test

Expressions and polynomials: 10 questions

Questions
10
Timer
None
No calculator
None
  • Check each answer as you go and read the working before the next question.
  • New numbers every time, so a second run tests the skill rather than your memory.
  • The formula sheet and calculator sit in the toolbar, as they do on the real test.

No account or email needed.

That is a different kind of difficulty from most of the test. Nobody loses these marks because the arithmetic is hard, since the numbers are small. Marks go missing on signs: a minus that only reached the first term in the brackets, a middle term that never got multiplied, "5 less than 3n" written as 5 − 3n. The practice set is built around those slips.

Expressions are the first half of "algebraic problem solving with expressions and equations", which GED Testing Service weights at about 30% of the test, the largest of the four reporting categories; the equations and inequalities topic is the other half. Thirty percent of about 46 questions is 13 or 14 items shared between the two, and an even split would put six or seven here. That is our arithmetic on the published weight, since no count per topic is published.

Skills in this set: Evaluating an expression for given values · Writing an expression from a description · Combining like terms · Adding and subtracting polynomials · Multiplying two binomials · Factoring out the greatest common factor · Factoring a quadratic trinomial

What the test asks

The Assessment Guide for Educators lists these skills as A.1.a through A.1.g. A.1.a is the housekeeping: combining, factoring, expanding and multiplying linear expressions with rational coefficients. A.1.b and A.1.e are evaluation, plugging integer values into a linear expression and then into a polynomial. A.1.c and A.1.g are translation, turning a sentence or an everyday situation into an expression. A.1.d is polynomial arithmetic: adding, subtracting and multiplying, including the product of two binomials, and dividing polynomials that factor. A.1.f is factoring on its own. Three more indicators, A.1.h through A.1.j, repeat the same jobs for algebraic fractions.

The situations are the ones you would meet on a bill. A gym charges a joining fee and a monthly rate; a print shop charges a setup fee plus a price per shirt; a rug is 7 feet longer than it is wide and the question wants its area as a polynomial. Pure symbol questions appear too, usually as "which expression is equivalent to" with four choices. Fill-in-the-blank items can ask you to type an answer, with an on-screen character selector for symbols, and drop-down items can ask for the common factor and the factored form in one sentence.

Much of this suits the opening no-calculator section, about five questions long, because a calculator adds nothing to combining like terms or multiplying (x + 4)(x − 2). Our practice set treats every item in this topic as a no-calculator item. The numbers are kept small for the same reason, so what the questions measure is care with signs and structure rather than arithmetic stamina.

The mistakes this set is built to catch

Each wrong answer in the practice set is the result of one specific slip, and the explanation names it. These are the ones that come up most in this topic.

1Letting a sign fall off a term

In 7x + 4 − 3x − 9 the sign in front of a term belongs to that term, so the x-terms are 7x and −3x, which give 4x, and the plain numbers are +4 and −9, which give −5. Combining 7 and 3 to get 10x, or 4 and 9 to get 13, are the two most common wrong answers, and both come from reading the sign as a separator. Evaluation has the same slip: n = −2 in 5n − 3 works only if you write 5(−2) − 3, brackets in.

2Flipping only the first sign when subtracting

Subtracting a polynomial means subtracting all of it. In (4x² + 3x − 5) − (x² − 2x + 7), the minus changes every term in the second bracket to −x², +2x and −7, giving 3x² + 5x − 12. Flipping only the x² and adding the other two terms as written gives x instead of 5x in the middle and 2 instead of −12 at the end. Rewrite the second bracket with every sign flipped before you collect anything.

3Skipping the middle term in a binomial product

(x + 4)(x − 2) is not x² − 8. First times first and last times last are only two of the four products; the outer and inner products, −2x and 4x, combine into the middle term 2x, and the full answer is x² + 2x − 8. The choices also offer x² − 2x − 8, with the middle sign wrong, and a version where the constants were added instead of multiplied. A check with x = 1 settles it: (5)(−1) = −5, and only x² + 2x − 8 gives −5.

4Writing "5 less than" in the wrong order

Five less than 3 times a number is 3n − 5. The words put the 5 first, so 5 − 3n looks right and is wrong: less than tells you to start from 3n and take 5 away. Cost situations set the same trap. A $30 setup charge plus $8 per shirt is 8s + 30, and the wrong answers charge the setup fee on every shirt, 38s, or multiply the shirts by 30. Ask which amount happens once and which happens every time, then test your expression with s = 2.

A worked example

A rectangular rug has a length of (x + 7) feet and a width of (x − 3) feet. Which polynomial gives the area of the rug in square feet?

  1. Write the area as a product

    The area of a rectangle is length times width, and both dimensions are binomials, so the area is the product of the two brackets.

    A = (x + 7)(x − 3)

  2. Multiply the first terms and the outer terms

    Every term in the first bracket multiplies every term in the second. Start with the x: it multiplies x and then −3.

    x · x = x² and x · (−3) = −3x

  3. Multiply the inner terms and the last terms

    Now the 7 does the same job, multiplying x and then −3. Keep the sign attached, because 7 times a negative is negative.

    7 · x = 7x and 7 · (−3) = −21

  4. Combine like terms and check

    The x-terms, −3x and 7x, add to 4x. To check, try x = 5: the rug would be 12 feet by 2 feet, an area of 24, and the polynomial gives 25 + 20 − 21 = 24 as well.

    x² − 3x + 7x − 21 = x² + 4x − 21; check: (5 + 7)(5 − 3) = 24 and 5² + 4(5) − 21 = 24

Answer: x² + 4x − 21 square feet

How to practice it

  1. Check every rewrite with a number. Pick something easy such as x = 2, put it into the original expression and into your answer, and compare. If the values differ, something changed along the way, and a sign error shows up long before rereading would find it. The answer explanations in our set end with this check.
  2. Sort the terms before you combine them. Underline the x² terms once and the x terms twice, leave the plain numbers alone, and take each sign along with its term. Writing the sorted groups on their own line, such as (7x − 3x) + (4 − 9), makes it almost impossible to add a plain number onto an x-term.
  3. Multiply binomials in a two-by-two box. Put one bracket across the top and the other down the side, and fill each cell with the product of its row and column. The two diagonal cells are always the like terms that make the middle term, so nothing gets skipped and the signs stay visible.
  4. Factor by listing, then multiply back. For x² + 2x − 15, list the pairs that multiply to −15 (1 and −15, −1 and 15, 3 and −5, −3 and 5) and pick the pair that adds to 2: −3 and 5, so the factors are (x − 3)(x + 5). Wrong pairs multiply to the right constant but add to the wrong middle number, and expanding your answer catches them.

Frequently asked questions

Do you have to factor on the GED?

Yes, factoring polynomial expressions is its own indicator, A.1.f, and A.1.d lists dividing polynomials that factor, so a question can ask for the factored form of x² + 5x + 6 directly. Pulling out a common factor is the version you will meet most. When the task is to solve a quadratic rather than to factor one, the quadratic formula on the formula sheet is an alternative route.

Is FOIL on the GED?

The word never appears in the official guide, but the skill does: A.1.d includes the product of two binomials, which is what FOIL is a memory aid for. Use whatever method gets you all four products, whether FOIL, a box grid or the distributive property written out twice. The wrong choices are built from the products people skip, so the method matters less than finding all four.

Will I have to type an expression instead of choosing one?

Possibly. The official item-type descriptions say fill-in-the-blank items can ask for a number or an equation typed with keyboard symbols or the on-screen character selector, and drop-down items embed the choices in a sentence. Multiple choice with four options is still the main format, so practicing the typed form is cheap insurance, which is why some items in our set ask you to enter an answer.

Are algebraic fractions on the GED math test?

Yes, in principle. Indicators A.1.h, A.1.i and A.1.j cover adding, subtracting, multiplying and dividing rational expressions, evaluating them for integer values, and writing them from a description. Our set concentrates on A.1.a through A.1.g, the polynomial skills the fraction versions are built on. GED Testing Service does not say how often the fraction versions appear.

Sources

Figures on this page were checked against these sources on the dates shown.

  1. Assessment Guide for Educators: Mathematical Reasoning · GED Testing Service · checked September 13, 2026
  2. Mathematics Formula Sheet (2026-02 revised) · GED Testing Service · checked September 13, 2026

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