Polynomial manipulation and algebraic division Quiz

1. Expand and simplify $(x+3)(x-2)(x+1)$.

• A. $x^3+6x^2-5x-6$
• B. $x^3+2x^2-5x-6$
• C. $x^3+2x^2+5x-6$
• D. $x^3-2x^2-5x+6$

2. Factorise $4x^2-25$.

• A. $(4x-5)(x+5)$
• B. $(2x-5)^2$
• C. $(4x+5)(x-5)$
• D. $(2x-5)(2x+5)$

3. Divide $x^3-2x^2-5x+6$ by $(x-3)$. What is the quotient?

• A. $x^2+x-2$
• B. $x^2-x-2$
• C. $x^2+x+2$
• D. $x^2-5x+10$

4. What is the remainder when $2x^3-5x^2+4x-7$ is divided by $(x-3)$?

• A. $-7$
• B. $0$
• C. $14$
• D. $7$

5. Factorise completely $x^3+x^2-9x-9$.

• A. $(x+1)(x^2-9)$
• B. $(x+1)(x-3)(x+3)$
• C. $(x-1)(x-3)(x+3)$
• D. $x(x+1)(x-9)$