Test your understanding of polynomial definitions, division, the Remainder Theorem, and the Factor Theorem.
1. State the degree and leading coefficient of $P(x)=4x^6-2x^3+x-5$. (2 marks)
2. Find the remainder when $x^3+3x^2-2x+1$ is divided by $(x-1)$. (2 marks)
3. Use the Factor Theorem to show that $(x+2)$ is a factor of $x^3+2x^2-5x-6$. (2 marks)
4. Fully factorise $x^3-7x+6$. (3 marks)