CBSE Class 10 Answered

By division theorem of Algorithm, we know that

p(x) = q(x).g(x) + r(x)

3x³+x²+2x+5 = (3x- 5).g(x) + 9x + 10

3x³+x² - 7x - 5 = (3x-5).g(x)

So, g(x) = (3x³+x² - 7x - 5)/ (3x - 5)

               = x² + 2x + 1

For the second question, substitute x  = -1 in the polynomial P(x)=3x³-5x²-11x-3 as it is given that -1 is the zero of the polynomial. The polynomial will reduce down to a quadratic polynomial. Equate it to zero and factorise to get the remaining two zeroes.