Class IX Holidays Home work Polynomials Assignment

1.        Find the value of x³ + y³ – 12xy + 64 when x + y = –4.
2.       If x = 2y + 6, then find the value of x³ – 8y³ – 36xy – 216.
3.      The polynomials kx³ + 3x² – 8 and 3x³ – 5x + k are divided by x + 2. If the remainder in each case is the same, find the value of k.
4.      Find the values of a and b so that the polynomial x³ + 10x² + ax + b has (x – 1) and          (x + 2) as factors.
5.      Find the values of p and q, if the polynomial x⁴ + px³ + 2x² – 3x + q is divisible by the polynomial x² – 1.
6.       If x – 3 is a factor of x² – kx + 12, then find the value of k. Also, find the other factor for this value of k.
7.      Find the value of k so that 2x – 1 be a factor of 8x⁴ + 4x³ – 16x² + 10x + k.
8.       If ax³ + bx² + x – 6 has (x + 2) as a factor and leaves a remainder 4 when divided by x – 2, find the values of a and b.
9.     If the polynomial P(x) = x⁴ – 2x³ + 3x² – ax + 8 is divided by (x – 2), it leaves a remainder 10. Find the value of a.
10. If both (x – 2) and ( x − 1/2 ) are factors of px² + 5x + r, show that p = r.
11. Find the value of a if (x + a) is a factor of x⁴ – a²x² + 3x – a.
12. Factorise by splitting the middle term : 9(x – 2y)² – 4(x – 2y) – 13.
13. Find the remainder obtained on dividing 2x⁴ – 3x³ – 5x² + x + 1by x - 1/2.
14. The polynomial p(x) = x⁴ – 2x³ + 3x² – ax + 3a – 7 when divided by x + 1, leaves the remainder 19. Find the value of a. Also, find the remainder when p(x) is divided by x + 2 
15. Without actual division prove that (x – 2) is a factor of the polynomial 3x³ – 13x² + 8x + 12. Also, factorise it completely.