BASIC OPERATION AND FACTORISATION (CDS)

Total Questions: 77

31. Let f(x) and g(x) be two polynomials (with real coefficients) having degrees 3 and 4 respectively. What is the degree of f(x) g(x) ? [2017 (II) Evening Shift]

Correct Answer: (b) 7
Solution:

32. Solve the following equation [2017 (II) Evening Shift]

Correct Answer: (a)
Solution:

33. Solve the following equation [2017 (II) Evening Shift]

Correct Answer: (a)
Solution:Given equation is

34. Solve the following equation [2017 (II) Evening Shift]

Correct Answer: (c) 1
Solution:If ab + bc + ca = 0, then what is the value of



35. Solve the following equation [2017 (II) Evening Shift]

Correct Answer: (b)
Solution:

36. If 5x² + 5x² - 6x + 9 is divided by (x + 3) then the remainder is [2017 (II) Evening Shift]

Correct Answer: (d) - 63
Solution:We have,

37. The quotient of 8x³ - y³ when divided by 2xy + 4x² + y² is ? [2017 (II) Evening Shift]

Correct Answer: (c) 2x − y
Solution:We have,

38. If (x + 2) is a common factor of x² + ax + b and x²³ + bx + a , then the ratio a : b is equal to [2017 (II) Evening Shift]

Correct Answer: (a) 1
Solution:We have, x + 2 is factor of x² + ax + b

39. The product of the polynomials (x + 2) (x - 2), (x³ - 2x² + 4x - 8) and (x³ + 2x² + 4x + 8) is [2017 (II) Evening Shift]

Correct Answer: (b) (x⁴ - 16)²
Solution:Let f (x) be the product of given polynomials. Then,

40. The factors of x(x + 2) (x + 3) (x + 5) - 72 are [2017 (II) Evening Shift]

Correct Answer: (c) (x - 1), (x + 6) and (x² + 5x + 12)
Solution:Let,