SAT Math skill page

SAT Polynomials Practice

Use structure in expressions so factoring and expanding feel predictable instead of messy.

Practice polynomials in Dolphin SAT Practice questions

12-18 min practice time3 questions on pageAdvanced Math

Practice time12-18 min

Practice questions3 questions

Best forAdvanced Math

What this tests

What to know for this SAT skill

Combine like terms in polynomial expressions
Expand products of binomials
Factor simple quadratics
Recognize equivalent polynomial forms

How do you choose a polynomial factoring method?

Look for a common factor before choosing a trinomial method. Then check what the question requests: a factor is an expression, while a solution is a value that makes an equation true.

What should you factor out first?

Find the greatest common factor of every term, including any shared variable powers. Write it outside parentheses and divide each term by it to form the remaining polynomial. Keep that outside factor in the final expression; removing it would change the value. Recheck the polynomial inside before choosing the next method.

What if the leading coefficient is not 1?

For an integer-coefficient trinomial ax² + bx + c, after removing the common factor, the ac method looks for integers whose product is a times c and whose sum is b. Split bx into two terms with those coefficients, then factor by grouping. The pair is used to split the middle term, not automatically as the constants in the final binomials. Multiply the factors back to check every coefficient. Not every trinomial factors into integer-coefficient binomials.

When can you set factors equal to zero?

Only use the zero-product property when a product equals zero. Factoring an expression alone does not create an equation. If solving an equation, first rearrange it so one side is zero, factor the other side, and consider each variable-containing factor. Do not divide away a factor that could be zero: that can lose a solution. Check the resulting values in the original equation.

References: OpenStax: common factors and the ac method and OpenStax: the zero-product property. Guidance reviewed October 7, 2026.

Dolphin practice questions

Practice your skill

Question 1 of 3Easy

Which expression is equivalent to

3 x^{2}

5 x^{2}

- 2x?

$8 x^{2} - 2 x$
8x - 2x
$6 x^{2}$
$3 x^{4} - 2 x$

Show answer and solution

Correct answer $A .8 x^{2} - 2 x$

Solution walkthrough

Combine only like terms: $3 x^{2}$ + $5 x^{2}$ = $8 x^{2}$ , while -2x remains separate.

Question 2 of 3Medium

Which expression is equivalent to (x + 4)(x - 3)?

$x^{2} + x - 12$
$x^{2} - x + 12$
$x^{2} + 7 x - 12$
$x^{2} - 12$

Show answer and solution

Correct answer $A . x^{2} + x - 12$

Solution walkthrough

Multiply each term: $x^{2}$ - 3x + 4x - 12 = $x^{2}$ + x - 12.

Question 3 of 3Hard

Which expression is a factor of

x^{2}

- 9x + 20?

x - 4
x + 4
x - 9
x + 20

Show answer and solution

Correct answerA. x - 4

Solution walkthrough

The numbers that multiply to 20 and add to -9 are -4 and -5, so the expression factors as (x - 4)(x - 5).

Avoid these traps

Common mistakes on this skill

Combining terms with different powers

Only like terms with the same variable part and exponent can be combined by adding coefficients.

Distributing a negative sign incompletely

A negative factor changes every term inside the parentheses.

Study plan

How to practice this skill in Dolphin

Arrange terms by descending exponent and identify like terms.
Use distribution or factoring one stage at a time, preserving every sign.
Expand the result or test multiple values to check the rewrite.

Practice polynomials in Dolphin SAT

Related practice

Build the surrounding skills

Skill cluster

Keep practicing SAT Math

FAQ

Questions about SAT Polynomials Practice

What are like terms?

They have identical variable factors raised to identical powers; only their coefficients may differ.

How do I check a polynomial factorization?

Multiply the factors back together and confirm that the original polynomial is recovered.