Question

1.Using remainder theorem , find the value of k if on dividing to 2x^3 + 3x^2 - kx +5 by x-2 , leaves a remainder 7

2. When x^3 + 3x^2 - kx -4 is divided by x-2 the remainder is k , find the value of k

3. Use factor theorem to factorise the polynomial x^3- 13x-12 completely

4. Using the remainder theorem factorise completely the following polynomial 3x^3 +2x^2 -19x +6

5. What no. should be subtracted from 2x^3 - 5x^2 +5x so that the resulting polynomial has a factor to x-3​

Answer 1

Answer:

2x^3 - 3x^2 - 17x + 30

= 2x^3 - 4x^2 +x^2 -2x - 15x + 30

=2x^2(x-2) +x(x-2) -15(x-2)

=(x-2)(2x^2 +x -15)

=(x-2)(2x^2 +6x -5x -15)

=(x-2)(2x(x+3) -5(x+3))

=(x-2)(x+3)(2x-5)