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Study guides › Level 8 · Algebra 2

Remainders without long division

Level 8 · Algebra 2 · for questions like “What is the remainder when x³ − 2x + 5 is divided by (x − 2)?”

💡 The idea

The remainder theorem: dividing a polynomial p(x) by (x − k) leaves the remainder p(k).

🪜 The steps

  1. Read k from the bracket: (x − 2) means k = 2.
  2. Put x = k into the polynomial.

✏️ Worked examples

1. x³ − 2x + 5, divided by (x − 2): 8 − 4 + 5 = 9.

2. x³ + x² − 4, divided by (x − 1): 1 + 1 − 4 = −2.

⚠️ Watch out

🎯 Try these

  1. x³ − 3x + 1, divided by (x − 2)
  2. x³ + 2x² − x, divided by (x − 1)
  3. x³ − 10, divided by (x − 3)

Answers: 1) 3 2) 2 3) 17

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