Polynomials And Equations — Flashcards
Kerala Board · Class 10 · Mathematics
20 flashcards for Polynomials And Equations (Kerala Board Class 10 Mathematics) to test yourself on key terms and facts.
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What is the general identity for multiplying two binomials (x + a)(x + b)?
Answer
(x + a)(x + b) = x² + (a + b)x + ab Remember: - Coefficient of x = sum of constants (a + b) - Constant term = product of constants (ab) Example: (x + 3)(x + 5) = x² + 8x + 15 Here: a = 3, b = 5, so…
Calculate 38 × 32 using polynomial multiplication method.
Answer
Step 1: Write as binomials 38 × 32 = (30 + 8) × (30 + 2) Step 2: Apply (x + a)(x + b) = x² + (a + b)x + ab where x = 30, a = 8, b = 2 Step 3: Calculate = 30² + (8 + 2) × 30 + 8 × 2 = 900 + 10 × 30 +…
How do you multiply (x + a)(x - b)?
Answer
(x + a)(x - b) = x² + (a - b)x - ab Step-by-step derivation: 1. Treat (x - b) as (x + (-b)) 2. Apply general formula: (x + a)(x + c) = x² + (a + c)x + ac 3. Here c = -b, so: x² + (a + (-b))x + a(-…
What is the product (x - a)(x - b)?
Answer
(x - a)(x - b) = x² - (a + b)x + ab Key points: - Both terms are negative - Coefficient of x = -(sum of constants) - Constant term = product of constants (positive) Example: (x - 3)(x - 2) = x² - 5x…
Factorize x² + 5x + 6
Answer
Step 1: Find two numbers whose sum = 5 and product = 6 We need: a + b = 5 and ab = 6 Step 2: Think of factor pairs of 6 6 = 1 × 6 (sum = 7) ✗ 6 = 2 × 3 (sum = 5) ✓ Step 3: Write the factorization x²…
Factorize x² - 5x + 6
Answer
Step 1: Find two numbers whose sum = -5 and product = 6 We need: a + b = -5 and ab = 6 Step 2: Since product is positive, both numbers have same sign Since sum is negative, both numbers are negative …
Factorize x² + x - 6
Answer
Step 1: Find two numbers whose sum = 1 and product = -6 We need: a + b = 1 and ab = -6 Step 2: Since product is negative, numbers have opposite signs Factor pairs of 6: 1×6, 2×3 Step 3: Check combin…
How do you factorize x² + 27x + 180 when mental calculation is difficult?
Answer
When a + b and ab are large, use the difference formula: Step 1: We have a + b = 27 and ab = 180 Step 2: Calculate (a - b)² (a - b)² = (a + b)² - 4ab = 27² - 4(180) = 729 - 720 = 9 Step 3: Find a -…
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
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