If x+k is the GCD of x2−2x−15 and x3+27, find the value of k
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Rewrite the following polynomial in standard form.6x3+2x−x5−3x2.
Evaluate each of the following using suitable identities:(i) (104)3 (ii) (999)3
Find the value of each of the following polynomials at the indicated value of variables:(i) p(x)=5x2−3x+7at x=1 (ii) q(y)=3y3−4y+11at y=2(iii) p(t)=4t4+5t3−t2+6at t=a
Give an example of a monomial of degree 5.
If the zeroes of the polynomial x3−3x2+x+1 are a−b,a,a+b, find a and b.
Divide 3x2+x3−3x+5by x−1−x2, and verify the division algorithm.
If x+y+z=0 show that x3+y3+z3=3xyz.
Write the following cubes in expanded form:(i) (2x+1)3 (ii) (2a−3b)3 (iii) [23x+1]3 (iv) [x−32y]3