Polynomials — Flashcards
Gujarat Board · Class 9 · Mathematics
30 flashcards for Polynomials (Gujarat Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "Identify whether 3x² + 2x + 5 is"
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Identify whether 3x² + 2x + 5 is a polynomial. State the reason.
Answer
Yes, it is a polynomial. Reason: It contains variables with non-negative integer exponents (x² has exponent 2, x has exponent 1, and 5 is a constant with x⁰). All terms have coefficients and constants…
Is 4x - 3/x + 2 a polynomial? Explain why or why not.
Answer
No, it is NOT a polynomial. Reason: The term -3/x can be written as -3x⁻¹. Since the exponent of x is -1 (a negative integer, not a whole number), this expression does not qualify as a polynomial. Pol…
Find the degree of the polynomial p(x) = 7x⁵ - 3x³ + 2x - 8
Answer
Step 1: Identify all terms: 7x⁵, -3x³, 2x, -8. Step 2: Find the exponents: 5, 3, 1, 0. Step 3: The highest exponent is 5. Step 4: The degree of the polynomial is 5. Answer: 5…
Classify the polynomial 5x² - 2x + 3 by degree type.
Answer
Step 1: Find the degree = 2 (highest power of x). Step 2: Match with classification: Degree 2 = Quadratic polynomial. Answer: This is a quadratic polynomial. Other classifications: Linear (degree 1), …
Classify x³ - 2x² + x - 5 as monomial, binomial, or trinomial, AND by degree.
Answer
Step 1: Count the terms: x³, -2x², x, -5 = 4 terms. Step 2: With 4 terms, it's not monomial (1 term), binomial (2 terms), or trinomial (3 terms). It's a polynomial with 4 terms. Step 3: Degree = 3 (hi…
Write one example each of: (i) monomial of degree 4, (ii) binomial of degree 3, (iii) trinomial of degree 2
Answer
Step 1: Monomial (1 term) of degree 4: 7x⁴. Step 2: Binomial (2 terms) of degree 3: 2x³ - 5x. Step 3: Trinomial (3 terms) of degree 2: x² + 3x - 2. Note: Multiple answers are acceptable as long as ter…
Find the value of p(x) = 2x² + 3x - 5 at x = 2
Answer
Step 1: Substitute x = 2 into p(x). Step 2: p(2) = 2(2)² + 3(2) - 5. Step 3: p(2) = 2(4) + 6 - 5. Step 4: p(2) = 8 + 6 - 5. Step 5: p(2) = 9. Answer: 9…
Evaluate p(x) = x³ - 2x² + x + 1 at x = -1
Answer
Step 1: Substitute x = -1 into p(x). Step 2: p(-1) = (-1)³ - 2(-1)² + (-1) + 1. Step 3: p(-1) = -1 - 2(1) - 1 + 1. Step 4: p(-1) = -1 - 2 - 1 + 1. Step 5: p(-1) = -3. Answer: -3…
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