Polynomials — Flashcards
Punjab Board · Class 9 · Mathematics
32 flashcards for Polynomials (Punjab Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Evaluate p(x) = 2x² + 5x - 3 at x = 2"
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Evaluate p(x) = 2x² + 5x - 3 at x = 2
Answer
Step 1: Substitute x = 2 into p(x) Step 2: p(2) = 2(2)² + 5(2) - 3 Step 3: p(2) = 2(4) + 10 - 3 Step 4: p(2) = 8 + 10 - 3 Step 5: p(2) = 15 Answer: The value of the polynomial at x = 2 is 15…
Find the value of p(x) = x³ - 3x² + 2x - 5 at x = -1
Answer
Step 1: Substitute x = -1 into p(x) Step 2: p(-1) = (-1)³ - 3(-1)² + 2(-1) - 5 Step 3: p(-1) = -1 - 3(1) - 2 - 5 Step 4: p(-1) = -1 - 3 - 2 - 5 Step 5: p(-1) = -11 Answer: The polynomial equals -11 w…
Check if x = 3 is a zero of p(x) = x² - 5x + 6
Answer
Step 1: Substitute x = 3 into p(x) Step 2: p(3) = (3)² - 5(3) + 6 Step 3: p(3) = 9 - 15 + 6 Step 4: p(3) = 0 Conclusion: Since p(3) = 0, x = 3 IS a zero of the polynomial. Note: This means (x - 3) i…
Verify that x = -2 is a zero of p(x) = x³ + 5x² + 8x + 4
Answer
Step 1: Substitute x = -2 into p(x) Step 2: p(-2) = (-2)³ + 5(-2)² + 8(-2) + 4 Step 3: p(-2) = -8 + 5(4) - 16 + 4 Step 4: p(-2) = -8 + 20 - 16 + 4 Step 5: p(-2) = 0 Conclusion: Since p(-2) = 0, x = -…
Find the zero of the linear polynomial p(x) = 3x + 7
Answer
Step 1: Set p(x) = 0 Step 2: 3x + 7 = 0 Step 3: 3x = -7 Step 4: x = -7/3 Answer: The zero of p(x) is x = -7/3 Verification: p(-7/3) = 3(-7/3) + 7 = -7 + 7 = 0 ✓ Note: Every linear polynomial ax + b…
What is the degree of the polynomial p(x) = 4x⁵ - 3x³ + 2x - 7?
Answer
Step 1: Identify all terms and their exponents - 4x⁵ has exponent 5 - -3x³ has exponent 3 - 2x has exponent 1 - -7 has exponent 0 Step 2: Find the highest exponent Highest exponent = 5 Answer: The d…
Determine if (x - 1) is a factor of p(x) = x³ + 2x² - 5x + 2 using the Factor Theorem
Answer
Factor Theorem: (x - a) is a factor of p(x) if and only if p(a) = 0 Step 1: For (x - 1), we have a = 1 Step 2: Calculate p(1) Step 3: p(1) = (1)³ + 2(1)² - 5(1) + 2 Step 4: p(1) = 1 + 2 - 5 + 2 Step …
Use Factor Theorem: Find the value of k if (x + 2) is a factor of p(x) = x² + kx - 6
Answer
Factor Theorem: If (x + 2) is a factor, then p(-2) = 0 Step 1: Set up the equation p(-2) = 0 Step 2: (-2)² + k(-2) - 6 = 0 Step 3: 4 - 2k - 6 = 0 Step 4: -2k - 2 = 0 Step 5: -2k = 2 Step 6: k = -1 A…
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