I need help on solving this task:
When polynomial \(\displaystyle f(x) \) is divided by polynomial \(\displaystyle g_1(x)=2x-1 \), the remainder is 2, and when \(\displaystyle f(x) \) is divided by polynomial \(\displaystyle g_2(x)=x+2 \), the remainder is 3. Determine the remainder that is left when \(\displaystyle f(x) \) is divided by \(\displaystyle g_1(x) \cdot g_2(x) \).
\(\displaystyle f(x)=(2x-1)q_1(x) + 2 \\ f(x)=(x+2)q_2(x) + 3 \).
I don't know nothing about \(\displaystyle f(x) \) or \(\displaystyle q(x) \). The problem is that I don't know how to start here.
When polynomial \(\displaystyle f(x) \) is divided by polynomial \(\displaystyle g_1(x)=2x-1 \), the remainder is 2, and when \(\displaystyle f(x) \) is divided by polynomial \(\displaystyle g_2(x)=x+2 \), the remainder is 3. Determine the remainder that is left when \(\displaystyle f(x) \) is divided by \(\displaystyle g_1(x) \cdot g_2(x) \).
\(\displaystyle f(x)=(2x-1)q_1(x) + 2 \\ f(x)=(x+2)q_2(x) + 3 \).
I don't know nothing about \(\displaystyle f(x) \) or \(\displaystyle q(x) \). The problem is that I don't know how to start here.