Grade X - Polynomial: Very short, Short and Long Questions #SEE

 

Polynomial

Very Short questions: 

1.       State factor theorem and remainder theorem.

2.       If a polynomial f(x) is divided by (x-a), what will be its remainder?

3.       If a polynomial f(x) is divided by (x + 3), what will be its remainder?

4.       If (x-m) is a factor of polynomial p(x), what is the value of p(m)?

5.       If (x-3) is a factor of polynomial p(x), what is the value of p (3)? 

6.       Define division algorithm. 

Short Questions: 

1.       If x³-19x-30 = (x+2).Q(x), find Q(x) by using synthetic division.                                                [2071 R ]

2.       Find the remainder when 3 x³ -5 x² +2x – 3 is divided by x-2, using remainder theorem.  

3.       If f(x) = 4 x³ - 3 x² +3x + k is divided by x-2  and remainder is 12, find value of k.                                                                                                                         [2075 R ]

4.       If x-2 is a factor of  2 x³ - 6 x² – 5m -2. Find the value of m.

5.       If 2x-5 is a factor of 6 x³ – (k +6) x² + 2kx – 25, find the value of k.

Long Questions:

Solve:

1.          x³ - 3 x² -4x + 12=0                                                                          [SEE Model 2076 ]

2.          x³ = 7 x² – 36                                                                                                   [ 2071 S ]

3.          x³ -21 x – 20 = 0                                                                                               [ 2070 S ]

4.          3x³ = 7 x² – 4