MEDIUM
Earn 100

Verify if on dividing 34x-22x3-12x4-10x2-75 by 3x+7 we get quotient -4x3+2x2-8x+30 and remainder -285.

Important Questions on Polynomials

HARD
For real numbers p, q and a, if the polynomial x3-3px+2q is divisible by the polynomial x2+2ax+a2, then which
of the following is correct? 
MEDIUM
If (ax+b)x5+1(5x+1) is divisible by x2+1, then the value of 2a+3b is
HARD
The remainder when the polynomial 1+x2+x4+x6+.....+x22 is divided by 1+x+x2+x3+.....+x11 is
MEDIUM
If 3x2x3+5x2 is divided by x1+x2, then the remainder is
MEDIUM
Total number of pencils required are given by 4x4+2x3-2x2+62x-66.If each box contains  x2+2x-3,then find the number of boxes to be purchased.
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
MEDIUM
Divide the polynomial px=x4-5x+6 by the polynomial gx=2-x2 and write the quotient and remainder.
EASY
If the polynomial x4+2x3+8x2+12x+18 is divided by x2+5 and the remainder is in the form of px+q, find the value of p and q.
HARD

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

MEDIUM
C0Cr+C1Cr+1+C2Cr+2++Cn-rCn is equal to
MEDIUM
Polynomial x4+x3-2x2+x+1 is divided by x-1, the remainder will be
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 f(x)=3x2-x3-3x+5 by the polynomial g(x)x-1-x2and verify the division algorithm

MEDIUM

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

MEDIUM

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

EASY

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