Using remainder theorem, find the remainder when p(x) = x3 + 3x2 – 5x + 4 is divided by (x ‒ 2).

It is given in the question that,p (x) = x3 + 3x2 – 5x + 4Now, p (2) = (2)3 + 3 (2)2 – 5 (2) + 4= 8 + 12 – 10 + 4= 14

Q12 of 113 Page 71

Using remainder theorem, find the remainder when p(x) = x³ + 3x² – 5x + 4 is divided by (x ‒ 2).

It is given in the question that,

p (x) = x³ + 3x² – 5x + 4

Now, p (2) = (2)³ + 3 (2)² – 5 (2) + 4

= 8 + 12 – 10 + 4

= 14

Find the quadratic polynomial, the sum of whose zeros is ‒5 and their products is 6.

Find a cubic polynomial whose zeros are 3, 5 and ‒2.

Show that (x + 2) is a factor of f(x) = x³ + 4x² + x – 6.

If α, β, γ are the zeros of the polynomial p(x) = 6x³ + 3x² – 5x + 1, find the value of .