Question

If P(x) = 2x³ + 2x² + bx - 6 leaves remainder 36, when divided by (x-3) , find the value of b and hence factorise P(x).

Answer 1

Answer:

b = -10

Step-by-step explanation:

p(x) = 2x³ + 2x² + bx - 6

g(x) = x - 3

Zeroes of x - 3 = 3

Put x = 3 in p(x).

p(3) = 2(3)³ + 2(3)² + b(3) - 6 = 2(27) + 2(9) + 3b - 6 = 54 + 18 - 6 + 3b = 66 + 3b.

But, when p(x) is divided by g(x), the remainder is 36.

∴ p(3) = 36

Hence, 66 + 3b = 36 or, 3(22 + b) = 36 or, 22 + b = 36/3 = 12 or, b = 12 - 22 = -10.

Thus, b = -10.