1) It degree of the polynomial is
a) 0
b)1
c)any natural no:
d) not defined
2) If p(x) =x^2 - 2 square root 2x +1, then p(2square root 2) is equal to
a)0
b)1
c)4 square root 2
d)8 square root 2+1
3) If x^51 +51 is divided by x+1 then reminder is
a)0
b)1
c) 49
d)50
4) Check whether p(x)=x^3 -5x^2 +4x-3 is a multiple of g(x)=x-2
5)find the value of p, if (x+3) is a factor of polynomial 2x^2-3x^2 +p
6) factorise
a) x^3 - 6x^2 +11x -6
Answers
Answer:
5) x+3 = 0 => x = -3 p(-3) = 0
p(-3) = 2*(-3)² - 3(-3) + p = 0
=> 2*9 + 9 + p = 0
=> 18 + 9 + p = 0
=> 27 + p = 0
=> p = -27
4) for x-2 to be a multiple of the given expression,
p (2) has to be zero [ x-2 = 0 , x = 2 ]
therefore p(2) = 2³ - 5*2² + 4*2 - 3
=> 8 - 20 + 8 - 3
=> - 7 ≠ 0, hence x-2 is not a multiple of
x³ - 5x² + 4x - 3
3) let x+1 = 0 => x = -1
when x⁵¹ + 51 is divided by x+1, the remainder
has to be equal to p(-1)
=> p(-1) = (-1)⁵¹ + 51
=> p(-1) = -1 + 51 [ when - 1 is raised to odd exponent, it remains as -1 ]
=> p(-1 ) = 50
therefore the remainder when x⁵¹ + 51 is divided by x+1 is + 50
Answer:
Answer:
5) x+3 = 0 => x = -3 p(-3) = 0
p(-3) = 2*(-3)² - 3(-3) + p = 0
=> 2*9 + 9 + p = 0
=> 18 + 9 + p = 0
=> 27 + p = 0
=> p = -27
4) for x-2 to be a multiple of the given expression,
p (2) has to be zero [ x-2 = 0 , x = 2 ]
therefore p(2) = 2³ - 5*2² + 4*2 - 3
=> 8 - 20 + 8 - 3
=> - 7 ≠ 0, hence x-2 is not a multiple of
x³ - 5x² + 4x - 3
3) let x+1 = 0 => x = -1
when x⁵¹ + 51 is divided by x+1, the remainder
has to be equal to p(-1)
=> p(-1) = (-1)⁵¹ + 51
=> p(-1) = -1 + 51 [ when - 1 is raised to odd exponent, it remains as -1 ]
=> p(-1 ) = 50
therefore the remainder when x⁵¹ + 51 is divided by x+1 is + 50