Algebraic Expressions And Polynomials
NIOS · Class 10 · Maths
Flashcards for Algebraic Expressions And Polynomials — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allSimplify: 3x² + 5x - 2x² + 7x - 4
Answer
Step 1: Group like terms → (3x² - 2x²) + (5x + 7x) - 4 Step 2: Combine like terms → x² + 12x - 4 Answer: x² + 12x - 4 Key Strategy: Always collect like terms first - terms with same variables and sam…
Find the degree of: 4x³y² - 2x²y⁴ + 7xy - 3
Answer
Step 1: Find degree of each term - 4x³y²: degree = 3 + 2 = 5 - 2x²y⁴: degree = 2 + 4 = 6 - 7xy: degree = 1 + 1 = 2 - 3: degree = 0 Step 2: Highest degree = 6 Answer: Degree is 6 Remember: Degree of …
Evaluate 2x³ - 5x² + 3x - 1 for x = 2
Answer
Step 1: Substitute x = 2 2(2)³ - 5(2)² + 3(2) - 1 Step 2: Calculate powers 2(8) - 5(4) + 3(2) - 1 Step 3: Multiply 16 - 20 + 6 - 1 Step 4: Add/subtract from left to right 16 - 20 + 6 - 1 = 1 Answe…
Is x = -2 a zero of x² + x - 2?
Answer
Step 1: Substitute x = -2 into the polynomial P(-2) = (-2)² + (-2) - 2 Step 2: Calculate P(-2) = 4 - 2 - 2 = 0 Step 3: Since P(-2) = 0, x = -2 is a zero. Answer: Yes, x = -2 is a zero. Definition:…
Add: (3x² - 4x + 1) + (2x² + 7x - 5)
Answer
Step 1: Remove brackets 3x² - 4x + 1 + 2x² + 7x - 5 Step 2: Group like terms (3x² + 2x²) + (-4x + 7x) + (1 - 5) Step 3: Add like terms 5x² + 3x - 4 Answer: 5x² + 3x - 4 Strategy: Arrange in column…
Subtract: (5x³ - 2x + 4) - (3x³ + x² - 7x + 1)
Answer
Step 1: Distribute the negative sign 5x³ - 2x + 4 - 3x³ - x² + 7x - 1 Step 2: Group like terms (5x³ - 3x³) + (-x²) + (-2x + 7x) + (4 - 1) Step 3: Combine 2x³ - x² + 5x + 3 Answer: 2x³ - x² + 5x + 3…
Multiply: 3x(2x² - 5x + 1)
Answer
Step 1: Distribute 3x to each term 3x × 2x² - 3x × 5x + 3x × 1 Step 2: Use laws of exponents 6x³ - 15x² + 3x Answer: 6x³ - 15x² + 3x Rule: When multiplying powers of same base, add the exponents: x…
Multiply: (x + 3)(2x - 1)
Answer
Step 1: Use FOIL method First: x × 2x = 2x² Outer: x × (-1) = -x Inner: 3 × 2x = 6x Last: 3 × (-1) = -3 Step 2: Combine all terms 2x² - x + 6x - 3 Step 3: Simplify 2x² + 5x - 3 Answer: 2x² + 5x - 3…
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