Given equation of which contains variables raised to the power 4, we use the remainder theorem to solve for that variable.

1. Polynomials Q2

2. Qn: Polynomials
(a) 2.5 (b) -5.5
(c) 3.5 (d) 6.5
x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4,
divided by x + 1 leaves remainder 3, find b.

3. Soln: Polynomials
Let f(x) = x4 – ax3 + bx2 – cx + 8
f(1) = 4
1 – a + b – c + 8 = 4
–a + b – c = - 5 ...... Eqn (1)
f(–1) = 3
1 + a + b + c + 8 = 3
a + b + c = - 6 ...... Eqn (2)
x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4,
divided by x + 1 leaves remainder 3, find b.

4. Soln: Polynomials
Adding Equation (1) and (2) we have
2b = -11,
or b = -5.5
Answer choice (b)
x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4,
divided by x + 1 leaves remainder 3, find b.