POLYNOMIALS
Practice Questions – Class IX
- Find the remainder when x3-ax2+6x-a is divided by x-a.
- Find the value of a and b so that the polynomial x3+10x2+ax+b is exactly divisible by (x-1) as well as by (x+2)
- Find the value of ‘a’ so that x+6 is a factor of x3+3x2+4x+a
- Show that (x+a) is a factor of xn+an for any odd positive integer n.
- Find the value of p if (x-p) is a factor of the polynomial x6-px5+x4-px3+3x-p+2.
- Show that 3 is a zero of the polynomial x3-8x2+8x+21.
- Prove that x2+2x+3 has no zero.
- Find the integral zeroes of the polynomial 2x3+5x2-5x-1.
- Find the values of a and b so that the polynomial x3-ax2-13x+b has (x-1) and (x+3) as factors.
- If x3+mx2+nx+6 has (x-2) as a factor and leaves remainder 3 , when divided by (x-3) , find the values of m and n.
- Find the value of p and q so that x-1 and x+1 are factors of x4+px3+2x2-3x+q.
- Find a & b such that x+2 and x-2 are factors of the polynomials ax4+2x3-3x2+bx-4
- If x-3 and x-1/3 are both factors of ax2+5x+b, show that a=b
- Find the value of a3-8b3-36ab-216 when a = 2b+6
- The polynomials ax3+3x2-3 and 2x3-5x+a when divided by x-4 leaves the remainders p and q respectively. Find the value of a if 2p=q.
- Prove that (x+y) 3+(y+z) 3+(z+x) 3-3(x+y)(y+z)(z+x)=2(x3+y3+z3-3xyz)
- Show that x-y , y-z and z-x are factors of x2 (y-z)+y2 (z-x)+z2 (x-y)
- Find the value of p and q so that x-1 and x+1 are factors of x4+px3+2x2-3x+q.
- Find a & b such that x+2 and x-2 are factors of the polynomials ax4+2x3-3x2+bx-4
- If x-3 and x-1/3 are both factors of ax2+5x+b, show that a=b
- The polynomials ax3+3x2-3 and 2x3-5x+a when divided by x-4 leaves the remainders p and q respectively. Find the value of a if 2p=q.
- Let A and B be the remainders when polynomials x3+2x2-5ax-7 and x3+ax2-12x+6 are divided by x+1 and x-2 respectively. If 2A+B=6 , find the value of a.
- Without actually calculating the cubes , evaluate each of the following
