Question

Let a(x) = 2x ^ 4 + 7x ^ 3 + 2x ^ 2 + 5x - 4 and b(x) = x ^ 2 + 3x - 1 .When dividing a by b, we can findthe unique quotient polynomial qand remainder polynomial r thatsatisfy the following equation: (a(x))/(b(x)) = q(x) + (r(x))/(b(x)) where the degree of r(x) is lessthan the degree of b(x) .What is the quotient, q(x) ? q(x) = What is the remainder, r(x) ?​

Answer 1

Answer:

Correct option is

C

−

3

1

P(3)=9p+(q−1)3+6=2⇒9p+3q+1=0

P(4)=16p+(q−1)4+6=1⇒16p+4q+1=0

Solving these two equation

p=

12

1

,q=

12

−7

∴3p+q=

3

−1