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SAT Math: Polynomials (Drill 3)

Drill 3 · Math · Polynomials

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About This Drill

SAT Math: Polynomials (Drill 3) is a Math practice drill covering Polynomials. It contains 5 original questions developed by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT polynomial questions test polynomial operations, factoring strategies, identifying zeros from factored form, applying the Remainder Theorem, and determining end behavior from the degree and sign of the leading coefficient of a polynomial function.

Questions & Explanations

Question 1. What is the product of (x + 3)(x² − 2x + 4)?

  • A) x³ − x² − 2x + 12
  • B) x³ − 2x² + 4x + 3x² − 6x + 12
  • C) x³ + x² − 2x + 12 ✓
  • D) x³ + 5x² + 10x + 12

Explanation: Distribute: x(x² − 2x + 4) + 3(x² − 2x + 4) = x³ − 2x² + 4x + 3x² − 6x + 12 = x³ + x² − 2x + 12.

Question 2. If p(x) = 2x³ − 5x + 3, what is p(−1)?

  • A) 6 ✓
  • B) 0
  • C) −4
  • D) 8

Explanation: p(−1) = 2(−1)³ − 5(−1) + 3 = −2 + 5 + 3 = 6.

Question 3. A polynomial has zeros at x = 0, x = 2, and x = −5. What is the minimum degree of this polynomial?

  • A) 2
  • B) 3 ✓
  • C) 4
  • D) 5

Explanation: Each zero contributes at least one factor. Three zeros require at least degree 3: x(x − 2)(x + 5).

Question 4. What is the remainder when x³ + 2x² − x + 7 is divided by (x − 2)?

  • A) 17
  • B) 21 ✓
  • C) 7
  • D) 13

Explanation: By the Remainder Theorem, evaluate at x = 2: 8 + 8 − 2 + 7 = 21.

Question 5. The leading term of f(x) is −4x⁴. Which describes the end behavior?

  • A) As x → ±∞, f(x) → +∞
  • B) As x → ±∞, f(x) → −∞ ✓
  • C) As x → −∞, f(x) → −∞ and as x → +∞, f(x) → +∞
  • D) As x → −∞, f(x) → +∞ and as x → +∞, f(x) → −∞

Explanation: Even degree (4) with negative leading coefficient: both ends go to −∞.