Polynomials — Flashcards
Maharashtra Board · Class 9 · Mathematics
28 flashcards for Polynomials (Maharashtra Board Class 9 Mathematics) to test yourself on key terms and facts.
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Is 3x² + 5x - 2 a polynomial? Explain why or why not.
Answer
Yes, it is a polynomial. Reason: All variables have whole number powers (2, 1, and 0 for the constant term). The expression uses only addition, subtraction, and multiplication operations. Each term ha…
Is √y + 5 a polynomial? Show your reasoning.
Answer
No, it is NOT a polynomial. Reason: √y can be written as y^(1/2). Since the power 1/2 is not a whole number, this violates the polynomial definition. Polynomials require all variable powers to be whol…
Identify which expressions are NOT polynomials: (a) 1/y - 3, (b) x² + 2x + 1, (c) y^(-2) + 7, (d) m³ - 5m + 2
Answer
NOT polynomials: (a) 1/y - 3 = y^(-1) - 3 [negative power], (c) y^(-2) + 7 [negative power]. ARE polynomials: (b) x² + 2x + 1 [all whole number powers], (d) m³ - 5m + 2 [all whole number powers]. Rule…
Find the degree of the polynomial 5x⁴ - 3x² + 7x - 2.
Answer
Step 1: Identify all terms: 5x⁴, -3x², 7x, -2. Step 2: Find the power of x in each term: 4, 2, 1, 0. Step 3: The degree is the HIGHEST power = 4. Answer: The degree of the polynomial is 4.
What is the degree of the constant polynomial 15?
Answer
Step 1: Write the constant as a power of variable: 15 = 15 × 1 = 15 × x⁰. Step 2: The power of the variable is 0. Step 3: Therefore, the degree of any non-zero constant polynomial is 0. Answer: Degree…
Find the degree of the polynomial 3m³n⁶ + 7m²n³ - mn in two variables.
Answer
Step 1: For polynomials in multiple variables, find the sum of powers in each term. Term 1: 3m³n⁶ → sum = 3 + 6 = 9. Term 2: 7m²n³ → sum = 2 + 3 = 5. Term 3: mn = m¹n¹ → sum = 1 + 1 = 2. Step 2: The d…
Write p(x) = 2x + 5x³ - 7 + x² in standard form and identify all coefficients.
Answer
Step 1: Arrange terms in descending order of powers: 5x³ + x² + 2x - 7. Step 2: Standard form is 5x³ + x² + 2x - 7. Step 3: Identify coefficients: Coefficient of x³ = 5, Coefficient of x² = 1, Coeffic…
Write the polynomial 2m⁴ + 5m² - 3m - 8 in index form (showing all missing terms).
Answer
Step 1: Standard form: 2m⁴ + 5m² - 3m - 8. Step 2: Check for missing powers: Power 4 exists, power 3 is MISSING, power 2 exists, power 1 exists, power 0 exists. Step 3: Add the missing term with coeff…
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