Question
If polynomial P(x) = x3 - 3x2 +
5x-3 is divided by polynomial G (x) = x2 - 2, the quotient and remainder are:Solution
Dividend = Divisor × quotient + remainder x3 - 3x2 + 5x - 3 = (x2 - 2) × (x - 3) + (7x - 9) x3 - 3x2 + 5x - 3 = (x3 - 3x2 - 2x + 6) + (7x - 9) x3 - 3x2 + 5x - 3 = x3 - 3x2 + 5x - 3 LHS = RHS Hence by using the long division method, the quotient and remainder of the polynomial p(x) = x3 - 3x2 + 5x - 3 when divided by the polynomial g(x) = x2 - 2 are x - 3 and 7x - 9 respectively.
Find the value of ‘x’ in the given expression:
(49/16)x × (64/343)x-1 = 4/7
If √k + (1/√k) = 8, then find the value of k + (1/k).
What is the HCF of (x³ + 3x² - x - 3) and (x³ + 4x² + x - 6)?
If, 4x + y = 10, and 2xy = 8, and 4x > y, then find the value of 64x³ – y³.
Evaluate (998)3 without multiplying directly.
If, ( a + b = 12 ) and ( a² + b² = 80 ), then find the value of (a³ + b³). Â
If n = 3 + √2, then find the value of (n + 1/n)².
 If f(x) = 3x² − 7x + 5, find f(2a) − 4f(a).
If 2x + y = 10 and 3x - 2y = 5, find the value of x + y.
Relevant for Exams:
