MEDIUM
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If 2 and -2 are zeros of the polynomial f(x)=2x4-3x3-3x2+6x-2, then find the sum of all other zeros.

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Important Questions on Polynomials

EASY

Following polynomial Px is divided by Sx. Obtain quotient and remainder.

Px=23x2+5x+6, Sx=x+6

MEDIUM

Divide the polynomial px by the polynomial qx and find the quotient and remainder:

px=x3-3x2+5x-3 and qx=x2-2

MEDIUM

Divide the polynomial px by the polynomial gx, and find the quotient and the remainder.

px=x4-5x+6, gx=2-x2

EASY

Divide the polynomial px=x3-3x2+5x-3 by the polynomial gx=x2-2. Find the quotient and remainder.

MEDIUM

Find all zeroes of the polynomial 2x4-9x3+5x2+3x-1 if two of its zeroes are 2+3 and 2-3.

MEDIUM

Find the quotient and the remainder when Px=3x3+x2+2x+5 is divided by g(x)=x2+2x+1.

MEDIUM
If 3 and -3 are the zeroes of the polynomial 2x4-3x3-5x2+9x-3. Find the other two zeroes of the polynomial.
MEDIUM

Divide the polynomial f(x)=3x2-x3-3x+5 by the polynomial g(x)x-1-x2and verify the division algorithm

MEDIUM
If 4 is a zero of the cubic polynomial x3-3x2-10x+24, find its other two zeroes.
HARD

Find the quotient and the remainder when fx=2x3-3x2+5x-7 is divided by gx=x-3 using synthetic division.

HARD
The equation 166×56=8590 is valid in some base b10 (that is, 1, 6, 5, 8, 9, 0 are digits in base b in the above equation). Find the sum of all possible values of b10 satisfying the equation.
MEDIUM

Divide the polynomial px=x3-3x2+5x-3 by the polynomial gx=x2-2. Find the quotient and remainder.

HARD

On dividing   x3-3x2+x+2 by a polynomial gx ,the quotient and remainder were, x-2, -2x+4 respectively. Find gx.

EASY

By using division algorithm method find quotient and remainder when polynomial P(x)=x43x2+4x3 is divided by g(x)=x2+1x

MEDIUM
Divide 3x3+x2+2x+5 by 1+2x+x2.
MEDIUM
Prove that on dividing 4x3+3x2+2x-9 by x-1 the remainder is 0.
HARD
Find the number of ordered triples (x,y,z) of real numbers that satisfy the system of equation x+y+z=7; x2+y2+z2=27; xyz=5
HARD
The remainder when the polynomial 1+x2+x4+x6+.....+x22 is divided by 1+x+x2+x3+.....+x11 is