Polynomials — Flashcards

Answer

Step 1: Identify the highest power of x → x³ has power 3. Step 2: Degree = 3. Step 3: Since degree = 3, it's a cubic polynomial. Step 4: Count terms → 4 terms, so it's not a monomial, binomial, or tri…

Answer

For p(2): Step 1: Substitute x = 2 → p(2) = 3(2)² - 5(2) + 2. Step 2: Calculate → p(2) = 3(4) - 10 + 2 = 12 - 10 + 2 = 4. For p(-1): Step 1: Substitute x = -1 → p(-1) = 3(-1)² - 5(-1) + 2. Step 2: Cal…

Answer

Step 1: Substitute x = 3 in p(x). Step 2: p(3) = (3)² - 5(3) + 6. Step 3: Calculate → p(3) = 9 - 15 + 6 = 0. Step 4: Since p(3) = 0, x = 3 is a zero of the polynomial. Answer: Yes, x = 3 is a zero bec…

Answer

Step 1: Set polynomial equal to zero → 4x - 12 = 0. Step 2: Add 12 to both sides → 4x = 12. Step 3: Divide both sides by 4 → x = 3. Step 4: Verify by substituting → p(3) = 4(3) - 12 = 0 ✓. Answer: x =…

Answer

Step 1: For (x - 2) to be a factor, p(2) must equal 0. Step 2: Let p(x) = x³ - 3x² + 4x - 2. Step 3: Find p(2) → p(2) = (2)³ - 3(2)² + 4(2) - 2. Step 4: Calculate → p(2) = 8 - 12 + 8 - 2 = 2. Step 5: …

Answer

Step 1: Since (x + 1) is a factor, p(-1) = 0 by Factor Theorem. Step 2: Let p(x) = x³ + ax² + 2x + a. Step 3: Find p(-1) → p(-1) = (-1)³ + a(-1)² + 2(-1) + a. Step 4: Simplify → p(-1) = -1 + a - 2 + a…

Answer

Step 1: Find two numbers that multiply to 12 and add to -7. Step 2: Factors of 12: 1×12, 2×6, 3×4. Check: -3 + (-4) = -7 and (-3)×(-4) = 12 ✓. Step 3: Split middle term → x² - 3x - 4x + 12. Step 4: Gr…

Answer

Step 1: Find two numbers that multiply to (6×3) = 18 and add to 11. Step 2: Factors of 18: Check 9 + 2 = 11 and 9×2 = 18 ✓. Step 3: Split middle term → 6x² + 9x + 2x + 3. Step 4: Group → 3x(2x + 3) + …