SAT Math: Add, subtract, and multiply polynomials
28+ practice questions in Praczo
The concept, explained
- 1
To add or subtract polynomials, combine like terms — terms with identical variable and exponent. 3x² + 5x² = 8x², but 3x² + 5x cannot combine.
- 2
When subtracting, distribute the negative sign into every term of the second polynomial: (3x² + 2x) − (x² − 4x) = 3x² + 2x − x² + 4x = 2x² + 6x.
- 3
To multiply a polynomial by a monomial, distribute: 2x(3x² − 5) = 6x³ − 10x.
- 4
To multiply two binomials, use FOIL; for larger polynomials, distribute every term of the first polynomial to every term of the second.
- ✗ Forgetting to distribute the minus sign when subtracting polynomials.
- ✗ Adding exponents when they should be multiplied (x² · x³ = x⁵, not x⁶).
SAT-style practice
What is (3x² + 2x − 5) − (x² − 4x + 7)?
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