Question

divide p( x ) by g ( x) wherep (x) = x+3x^2-1 and g (x) =1+x .

Answer 1

$p(x) = x + 3x {}^{2} - 1 \\ = 3x {}^{2} + x - 1 \\ g(x) = 1 + x \\ = x+ 1 \\ g(x) = 0 \\ x + 1 = 0 \\ x = - 1 \\ remainder = p( - 1) \\ = 3 \times ( - 1) {}^{2} + ( - 1) - 1 \\ = 3 \times 1 - 1 - 1 \\ = 3 - 2 \\ = 1$