Question

3. When P(x) is divided by (x + 2), the remainder is 5 and when divided by (x - 2), the remainder is 13. Find the remainder when P(x) is divided by (x + 2)(x - 2).​

Answer 1

Hi,

Explanation:

P(x) divided by (x+2) give a remainder of 5

`P(x)=Q(x)*(x+2) +5\\`

Let's calculate the remainder of P(x) by (x-2) : when x=2

`P(2)=Q(2)*(2+2)+5 = 13\\4Q(2)=8\\Q(2)=2\\\\Q(x)=(x-2)*R(x)+2\\\\P(x)=(x+2)*Q(x)+5\\=(x+2)*((x-2)*R(x)+2)+5\\=(x+2)(x-2)*R(x)+2*(x+2)+5\\=(x+2)(x-2)*R(x) +2x+9\\\\Remainder\ is\ 2x+9\\`