Consider two polynomials P(x)=4x^(3)+ax^(2)+bx-5 and Q(x)=x^(2)+1. It is given that P(x) is divisible by x+1 and 2x+1.
(a) Find the values of a and b.
(b) Find the quotient and the remainder when P(x) is divided by Q(x).
(c) Solve (8x-1)Q(x)-2P(x)-9=0.

Question

Consider two polynomials P(x)=4x^(3)+ax^(2)+bx-5 and Q(x)=x^(2)+1. It is given that P(x) is divisible by x+1 and 2x+1.
(a) Find the values of a and b.
(b) Find the quotient and the remainder when P(x) is divided by Q(x).
(c) Solve (8x-1)Q(x)-2P(x)-9=0.

anonymous · Answer

The divisibility by x+1 and 2x+1 gives you two roots. So you know P(roots)=0 so now you have a system of equations. Two equations two unknows. You can solve for a and b

anonymous · Answer

4(-1)^(3)+a(-1)^(2)+b(-1)-5 = 0
4(-1/2)^(3)+a(-1/2)^(2)+b(-1/2)-5 = 0

anonymous · Answer

4(-1)^(3)+a(-1)^(2)+b(-1)-5 = 0
4(-1/2)^(3)+a(-1/2)^(2)+b(-1/2)-5 = 0

a-b=9---(1)
a-2b=-22---(2)

i can't get the answer

anonymous · Answer

That 22 should be positive.

anonymous · Answer

ok got it.