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GED Algebra Expressions: 25 Practice Questions to Simplify, Expand and Factor

An expression is algebra with no equals sign, so there’s nothing to solve. Your job is to tidy it up: group what matches, multiply things out, or pull out what’s shared. Think of it as sorting a messy drawer.

Start 25 expressions and polynomials questions

New questions every time you start. Come back as often as you like.

Updated September 25, 2026 · Lessons by Coach Crissy
Questions per set
25
Skills covered
7
Score-report category
Algebraic problem solving with expressions and equations · 30% of the test

Expressions and polynomials: 25 questions

Questions
25
Timer
None
No calculator
None

New questions every time you start. Do this set as many times as you like.

  • Check each answer as you go and read the working before the next question.
  • The formula sheet and calculator sit in the toolbar, as they do on the real test.

No account or email needed.

If a line like 7x + 4 − 3x − 9 looks like alphabet soup to you, you’re not the only one.

Tidying it works like sorting a junk drawer. Batteries go with batteries and pens go with pens. In algebra, the x-terms go together and the plain numbers go together, and that’s most of the job.

The catch? The numbers in these questions are small, so points get lost on signs instead. A minus gets dropped, a middle term goes missing, or “5 less than” ends up backward. The habits below fix most of it.

On this page you’ll get:

  • 25 practice questions (scroll up), new ones every time
  • How to turn words into algebra, like “5 less than twice a number”
  • Combining like terms, multiplying and factoring, step by step
  • The sign slips that cost the most points

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 GED expression questions look like

Many questions start in words, and the words don’t come in the order you write them. “5 less than twice a number” means: start with twice the number (2n), then take 5 away. So it’s 2n − 5. Think of a coupon: $5 less than the price is the price minus 5.

Cost stories work the same way. A print shop charges a $30 setup fee plus $8 per shirt, so s shirts cost 8s + 30. The fee happens once and the $8 happens with every shirt, so the $8 is the part that goes with the letter.

Combining like terms is the junk drawer again. In 7x + 4 − 3x − 9, the x-terms are 7x and −3x, which make 4x. The numbers are +4 and −9, which make −5. Carry each sign along with its term, and the tidy version is 4x − 5.

Multiplying two sets of parentheses is like handshakes between two couples: each person in the first pair shakes hands with each person in the second, so there are four handshakes. For (x + 4)(x − 2) those are x², −2x, 4x and −8. Combine the middle two and you get x² + 2x − 8.

Factoring runs that backward. For x² + 2x − 15, look for two numbers that multiply to −15 and add to 2. That’s −3 and 5, so the answer is (x − 3)(x + 5). Pulling out a number that every term shares, as in 6x + 9 = 3(2x + 3), is the version you’ll see most.

Questions with only symbols often ask “which expression is equivalent to”. Some ask you to type your answer or pick from drop-down menus. A calculator adds nothing here, so these fit the first five or so questions, which have no calculator.

How many questions? GED Testing Service doesn’t publish a count per topic. Expressions share the biggest scoring area, about 30% of the test, with equations, so our estimate is six or seven expression questions out of about 46.

The topics and area weights come from GED Testing Service’s official test guide. It doesn’t publish a question count per topic, so any count here is our estimate.

The 4 mistakes that cost the most points

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.

1Dropping the minus when you plug in a number

A minus sign sticks to its number like a price tag sticks to an item. If n = −2, write 5(−2) − 3 with the parentheses, which gives −13. Leave the parentheses off and the minus tends to fall away, which gives 7 instead.

2Flipping only the first sign when you subtract parentheses

Subtracting a set of parentheses is like returning a whole bag of groceries: everything in the bag comes off the bill. In (4x² + 3x − 5) − (x² − 2x + 7), every sign in the second set of parentheses flips, giving 3x² + 5x − 12. Rewrite the second set with its signs flipped before you combine anything.

3Losing the middle term when you multiply parentheses

(x + 4)(x − 2) has four handshakes, and the two in the middle (−2x and 4x) combine to 2x. The full answer is x² + 2x − 8, and x² − 8 is the common wrong one. To check, put x = 1 into both: (5)(−1) = −5, and only x² + 2x − 8 also gives −5.

4Writing “5 less than” backward

Five less than twice a number is 2n − 5, because you start from 2n and take 5 away. Writing 5 − 2n is the classic trap, and it’s usually one of the choices. Picture the coupon: you start with the price, then the $5 comes off.

One problem, worked out step by step

Worked example
Expressions and polynomials

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?

The working

  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 sets of parentheses.
    A = (x + 7)(x − 3)
  2. Multiply the first terms and the outer terms
    Every term in the first set of parentheses 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 get better at this, fast

  1. Check every rewrite with a number. Put a small value such as x = 2 into the original and into your answer. If the results differ, something changed along the way.
  2. Sort the terms before you combine them. Underline the x² terms once and the x terms twice, and carry each sign with its term.
  3. Multiply two sets of parentheses in a two-by-two box. Put one across the top and the other down the side, then fill each cell. The two diagonal cells are the like terms that make the middle term.
  4. After you factor, multiply the parentheses back out. If you don’t land on the expression you started with, the pair of numbers is off, so try the next pair.

Frequently asked questions

Do you have to factor on the GED?

Yes. A question can ask for the factored form of something like x² + 5x + 6, and pulling out a common factor is the version you’ll see most. When you need to solve a quadratic, the quadratic formula on the formula sheet is another route.

Is FOIL on the GED?

The word isn’t in the official guide, but multiplying two sets of parentheses is. Use FOIL, a box or the handshake picture, as long as you get all four products.

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

Possibly. Fill-in-the-blank items can ask you to type an answer using the keyboard or an on-screen symbol picker. Four-option multiple choice is still the main format.

Are algebraic fractions on the GED math test?

They’re listed in the official guide, but it doesn’t say how often they appear. Our set focuses on the skills algebraic fractions are built on.

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