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

Question bank3 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

Dolphin question bank

Practice your skill

Question 1 of 3Easy

Which expression is equivalent to 3x^2 + 5x^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: 3x^2 + 5x^2 = 8x^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

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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.