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 allSolve the substitution: Evaluate 1 - x^5 + 2x^6 + 7x when x = 1/2.
Answer
Step 1: Substitute x = 1/2 1 - (1/2)^5 + 2(1/2)^6 + 7(1/2) Step 2: Simplify powers = 1 - 1/32 + 2/64 + 7/2 = 1 - 1/32 + 1/32 + 7/2 Step 3: Cancel the middle terms = 1 + 7/2 = 9/2 Answer: 9/2 or 4 1…
Evaluate: 5x^3 + 3x^2 - 4x - 4 for x = 1.
Answer
Step 1: Substitute x = 1 5(1)^3 + 3(1)^2 - 4(1) - 4 Step 2: Simplify = 5 + 3 - 4 - 4 = 0 Answer: 0…
Is x = -1 a zero of x^3 + 3x^2 + 3x + 2? Show the check.
Answer
Step 1: Substitute x = -1 (-1)^3 + 3(-1)^2 + 3(-1) + 2 Step 2: Simplify = -1 + 3 - 3 + 2 = 1 Step 3: Compare with 0 1 is not 0 Answer: x = -1 is not a zero of the polynomial.
Is x = 1 a zero of x^4 - 4x^3 + 6x^2 - 4x + 1? Show the check.
Answer
Step 1: Substitute x = 1 (1)^4 - 4(1)^3 + 6(1)^2 - 4(1) + 1 Step 2: Simplify = 1 - 4 + 6 - 4 + 1 = 0 Answer: Yes, x = 1 is a zero of the polynomial.
Add the like terms: 2x + 3x.
Answer
Use the sum of like terms: 2x + 3x = (2 + 3)x = 5x Answer: 5x…
Find the result of 9x^2y^2 - 5x^2y^2.
Answer
Use the difference of like terms: 9x^2y^2 - 5x^2y^2 = (9 - 5)x^2y^2 = 4x^2y^2 Answer: 4x^2y^2…
Add the polynomials: -3x + 4 and 2x^2 - 7x - 2.
Answer
Step 1: Group like terms (-3x + 4) + (2x^2 - 7x - 2) Step 2: Combine like terms = 2x^2 + (-3x - 7x) + (4 - 2) = 2x^2 - 10x + 2 Answer: 2x^2 - 10x + 2…
Add: 5x + 3y - 3/4 and -2x + y + 7/4.
Answer
Step 1: Group like terms (5x - 2x) + (3y + y) + (-3/4 + 7/4) Step 2: Combine = 3x + 4y + 4/4 = 3x + 4y + 1 Answer: 3x + 4y + 1…
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