Question

(a) What will the quotient and remainder be on division of ax2+bx+c by px3+qx2+rx+s,
p≠ 0

Answer 1

The quotient will be zero.

The remainder will be ax² + bx + c

Step-by-step explanation:

Let

p(x)=ax^2+bx+cp(x)=ax

2+bx+c

And

h(x)=px^3+qx^2+rx+sh(x)=px

3+qx

2+rx+s , p\ne 0p

=0

Degree of polynomial p(x) = 2

Degree of polynomial h(x) = 3

Thus, the degree of polynomial h(x) is greater than the degree of polynomial p(x)

Therefore, if we divide p(x) with h(x), the division is not possible in the form we know as two polynomial can be divided only when the degree of the divisor is less than that of the dividend

Therefore in this case, the quotient will be zero

The remainder will be equal to the dividend which is ax^2+bx+cax

2

+bx+c

Hope this answer is helpful.

Q: If the remainder on division of x3 + 2x2 + kx + 3 by x – 3 is 21, find the quotient and the value of k. Hence, find the zeroes of the cubic polynomial x3 + 2x2 + kx – 18