" (1) "p(x)=2x^(3)-13x^(2)+23x-12,8(x)=2x-3

Divide the following polynomial p(x) by polynomial s(x) p(x)=2x^(3)-13x^(2)+23x-12,s(x)=2x-3

Check whether g(x) is a factor of p(x) by dividing the first polynomial by the second polynomial: (i) p(x) = 4x^(3) + 8x + 8x^(2) +7, g(x) =2x^(2) -x+1 , (ii) p(x) =x^(4) - 5x -2, g(x) =2-x^(2) , (iii) p(x) = 13x^(3) -19x^(2) + 12x +14, g(x) =2-2x +x^(2)

Using the remainder theorem , find the remainder , when p (x) is divided by g (x) , where p(x)=6x^(3)+13x^(2)+3,g(x)=3x+2 .

If f(x)=2x^(3)-13x^(2)+17x+12, find f(2) (ii) f(-3)

lim_(x rarr1)(x^(4)+3x^(3)-13x^(2)-27x+36)/(x^(2)+3x-4)

Using the Remainder Theorem, factorise each of the following completely: (i) 3x^3+2x^(2)-19x+6 (ii) 2x^(3)+x^2-13x+6 (iii) 3x^(3)+2x^2-23x-30 (iv) 4x^3+7x^2-36x-63 (v) x^3+x^2-4x-4

If f(x)=2x^(3)-13x^(2)+17x+12; Find f(-1) and f(2)

What must be subtracted from the polynomial f(x)=x^(4)+2x^(3)-13x^(2)-12x+21 so that the resulting polynomial is exactly divisible by x^(4)-4x+3?

Evaluate: lim_(x rarr -2) (2x^(3)-x^(2)-13x-6)/(3x^(2)+x-10) .