Algebra — Flashcards

Answer

Step 1: Identify a = 2, b = 15, c = 27 Step 2: Find ac = 2 × 27 = 54 Step 3: Find two numbers that multiply to 54 and add to 15 → 6 and 9 Step 4: Split middle term: 2x² + 6x + 9x + 27 Step 5: Group: 2…

Answer

Remainder Theorem: If p(x) is divided by (x - a), remainder = p(a) Here: divisor is (x + 1), so a = -1 Step 1: Substitute x = -1 in f(x) Step 2: f(-1) = (-1)³ + 3(-1)² + 3(-1) + 1 Step 3: f(-1) = -1 +…

Answer

Use Remainder Theorem: To find remainder without performing long division of polynomials Advantage: Quick and efficient method Example: Find remainder when p(x) = 2x⁴ - 6x³ + 3x² + 3x - 2 is divided b…

Answer

Identity: (a + b)² = a² + 2ab + b² Given: (3x + 4y)² Step 1: Identify a = 3x, b = 4y Step 2: Apply identity Step 3: a² = (3x)² = 9x² Step 4: 2ab = 2(3x)(4y) = 24xy Step 5: b² = (4y)² = 16y² Step 6: Co…

Answer

Formula: (a + b)² = a² + 2ab + b² Where: - a = first term - b = second term - a² = square of first term - 2ab = twice the product of both terms - b² = square of second term Quick Example: (2x + 3)² =…

Answer

Identity: a² - b² = (a + b)(a - b) Given: 36m² - 49n² Step 1: Identify perfect squares: 36m² = (6m)², 49n² = (7n)² Step 2: Rewrite: (6m)² - (7n)² Step 3: Apply identity with a = 6m, b = 7n Step 4: (6m…

Answer

Step 1: Write both polynomials in standard form (already done) Step 2: Arrange like terms vertically: 2x³ + 4x² - 3x + 5 + x² + 2x + 4 Step 3: Add like terms: - x³ terms: 2x³ - x² terms: 4…

Answer

Step 1: Distribute each term of first polynomial to second polynomial Step 2: 4x(2x² + 3x - 6) - 5(2x² + 3x - 6) Step 3: Calculate 4x × each term: 4x × 2x² = 8x³ 4x × 3x = 12x² 4x × (-6) = -24x …