Please tell me answers of practice set 10.2 (8th std mh board)
Answers
Question :- Tell me answers of practice set 10.2 (8th std mh board) .
Division of Polynomials Class 8 Practice Set 10.2 Question 1. Divide and write the quotient and the remainder.
i. (y² + 10y + 24) ÷ (y + 4)
ii. (p² + 7p - 5) ÷ (p + 3)
iii. (3x + 2x² + 4x³) ÷ (x - 4)
iv. (2m³ + m² + m + 9) ÷ (2m - 1)
v. (3x - 3x² - 12 + x4 + x3) ÷ (2 + x²)
vi. (a⁴ - a³ + a² - a + 1) ÷ (a³ - 2)
vii. (4x⁴ - 5x³ - 7x + 1) ÷ (4x - 1)
Solution :-
Points to remember in LONG METHOD DIVISION :-
⋆ Arrange the indices of the polynomial in descending order. Replace the missing term(s) with 0.
⋆ Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient.
⋆ Multiply the divisor by the first term of the quotient.
⋆ Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend. Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".
⋆ Repeat step 2 - 4 to find the second term of the quotient.
⋆ Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.
⋆ If the divisor is a factor of the dividend, you will obtain a remainder equal to zero. If the divisor is not a factor of the dividend, you will obtain a remainder whose index is lower than the index of the divisor.
Solution i) :-
y + 4 ) y² + 10y + 24 ( y + 6
y² + 4y
6y + 24
6y + 24
0
- Quotient = y + 6
- Remainder = 0 .
Solving rest by similar method we get,
Answer ii) :- (p² + 7p - 5) ÷ (p + 3)
- Quotient = p + 4 .
- Remainder = (-17) .
Answer iii) :- (3x + 2x² + 4x³) ÷ (x - 4)
- Quotient = 4x² + 18x + 75
- Remainder = 300 .
Answer iv) :- (2m³ + m² + m + 9) ÷ (2m - 1)
- Quotient = m² + m + 1
- Remainder = 10 .
Answer v) :- (3x - 3x² - 12 + x4 + x3) ÷ (2 + x²)
- Quotient = x² + x - 5
- Remainder = x - 2
Answer vi) :- (a⁴ - a³ + a² - a + 1) ÷ (a³ - 2)
- Quotient = a - 1
- Remainder = a² + a - 1
Answer vii) :- (4x⁴ - 5x³ - 7x + 1) ÷ (4x - 1)
- Quotient = x³ - x² - x/4 - 29/16 .
- Remainder = (-13/16) .
Learn more :-
given that under root 3 is irrational prove that 5 root 3 minus 2 is an irrational number
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