Multiple Choice

1. Factorise the quadratic expression $x^2 + 7x + 10$.

   $(x+3)(x+4)$

   $(x+2)(x+5)$

   $(x-2)(x-5)$

   $(x+1)(x+10)$

2. Factorise the quadratic expression $x^2 - 3x - 18$.

   $(x+9)(x-2)$

   $(x-6)(x+3)$

   $(x+6)(x-3)$

   $(x-9)(x+2)$

3. Factorise the quadratic expression $x^2 - 11x + 28$.

   $(x+4)(x+7)$

   $(x+2)(x+14)$

   $(x-4)(x-7)$

   $(x-2)(x-14)$

4. Factorise the expression $ax + ay + bx + by$.

   $a(x+y) + b(x-y)$

   $(a+b)(x+y)$

   $(a-b)(x+y)$

   $(a+x)(b+y)$

5. Factorise the quadratic expression $2x^2 + 5x + 3$.

   $(2x+3)(x+1)$

   $(x+1)(x+3)$

   $(2x-3)(x-1)$

   $(2x+1)(x+3)$

6. Factorise the expression $3x^2 - 6x + 4x - 8$.

   $(3x+2)(x-4)$

   $(3x-2)(x+4)$

   $(3x+4)(x-2)$

   $(3x-4)(x+2)$

7. Factorise the quadratic expression $x^2 + 13x + 36$.

   $(x+4)(x+9)$

   $(x+6)(x+6)$

   $(x-4)(x-9)$

   $(x+3)(x+12)$

8. Factorise the quadratic expression $3x^2 + 10x + 8$.

   $(3x+1)(x+8)$

   $(3x+2)(x+4)$

   $(3x+8)(x+1)$

   $(3x+4)(x+2)$

9. Factorise the expression $ab - ac + db - dc$.

   $(a-b)(c+d)$

   $(a-d)(b+c)$

   $(a+d)(b-c)$

   $(a+b)(c-d)$

10. Factorise the quadratic expression $x^2 - 6x - 16$.

    $(x-4)(x+4)$

    $(x+8)(x-2)$

    $(x-8)(x+2)$

    $(x-16)(x+1)$

11. Factorise the quadratic expression $4x^2 + 4x - 3$.

    $(4x+1)(x-3)$

    $(2x+3)(2x-1)$

    $(4x-1)(x+3)$

    $(2x-3)(2x+1)$

12. Factorise the expression $y^2 + 3y + xy + 3x$.

    $(y+3x)(y+1)$

    $(y+x)(y-3)$

    $(y+x)(y+3)$

    $(y-x)(y+3)$

13. Factorise the quadratic expression $m^2 - 2m - 35$.

    $(m-35)(m+1)$

    $(m+7)(m-5)$

    $(m+35)(m-1)$

    $(m-7)(m+5)$

14. Factorise the quadratic expression $5x^2 - 13x + 6$.

    $(5x-2)(x-3)$

    $(5x+3)(x+2)$

    $(5x-3)(x-2)$

    $(5x+2)(x+3)$

15. Factorise the expression $2p^2q - 2pr + 3pq - 3r$.

    $(2p-3)(pq+r)$

    $(2pq+r)(p-3)$

    $(2p+3)(pq-r)$

    $(2p+r)(q-3)$

16. Factorise the quadratic expression $a^2 - 12a + 27$.

    $(a-3)(a-9)$

    $(a-1)(a-27)$

    $(a+1)(a+27)$

    $(a+3)(a+9)$

17. Factorise the expression $6x^2 + 9x + 3$.

    $(6x+3)(x+1)$

    $3(2x+1)(x-1)$

    $3(2x+1)(x+1)$

    $3(2x+3)(x+1)$

18. Factorise the expression $x^3 - 4x^2 + 5x - 20$.

    $(x^2+5)(x-4)$

    $(x^2-5)(x+4)$

    $(x^2-4)(x+5)$

    $(x^2+4)(x-5)$

19. Factorise the quadratic expression $6y^2 - 7y - 5$.

    $(3y+5)(2y-1)$

    $(6y-1)(y+5)$

    $(6y+5)(y-1)$

    $(3y-5)(2y+1)$

20. Factorise the quadratic expression $k^2 + 8k + 15$.

    $(k+1)(k+15)$

    $(k-3)(k-5)$

    $(k+3)(k+5)$

    $(k-1)(k-15)$

21. Factorise the expression $12y^3 + 18y^2 - 10y - 15$ completely.

    $(6y^2 - 5)(2y + 3)$

    $(6y^2 - 5)(2y - 3)$

    $(12y^2 - 5)(y + 3)$

    $(6y^2 + 5)(2y - 3)$

22. Factorise the quadratic expression $m^2 - 5m - 84$ completely.

    $(m + 7)(m - 12)$

    $(m - 7)(m + 12)$

    $(m + 6)(m - 14)$

    $(m - 4)(m + 21)$

23. Factorise the quadratic expression $12k^2 - 23k + 10$ completely.

    $(4k + 5)(3k - 2)$

    $(6k - 5)(2k - 2)$

    $(4k - 5)(3k - 2)$

    $(4k - 1)(3k - 10)$

24. Factorise the quadratic expression $10x^2 + 13x - 30$ completely.

    $(10x - 6)(x + 5)$

    $(2x + 6)(5x - 5)$

    $(2x + 5)(5x - 6)$

    $(2x - 5)(5x + 6)$

25. Factorise the expression $4m^3 - 16m^2 + 3m - 12$ completely.

    $(4m^2 + 4)(m - 3)$

    $(2m^2 + 3)(2m - 4)$

    $(4m^2 - 3)(m + 4)$

    $(4m^2 + 3)(m - 4)$

26. What value of $c$ completes the square for the expression $x^2 + 14x + c$?

    $14$

    $49$

    $28$

    $7$

27. Which of the following is the correct form after completing the square for $x^2 - 8x$?

    $(x-4)^2$

    $(x-8)^2 - 64$

    $(x-4)^2 - 8$

    $(x-4)^2 - 16$

28. What term must be added to $x^2 + 8x$ to complete the square?

    $16$

    $64$

    $4$

    $8$

29. To complete the square for the expression $x^2 - 12x$, what constant term should be added?

    $36$

    $-6$

    $-36$

    $12$

30. Determine the term needed to complete the square for the quadratic expression $x^2 + 10x$.

    $25x$

    $25$

    $5$

    $100$

31. What constant should be added to $x^2 - 4x$ to make it a perfect square trinomial?

    $16$

    $-2$

    $4x$

    $4$

32. Complete the square for the expression $x^2 + 7x$. What term must be added?

    $\frac{7}{2}$

    $7$

    $\frac{49}{4}$

    $49$

33. To transform $x^2 - 9x$ into a perfect square trinomial, which value should be added?

    $\frac{81}{4}$

    $81$

    $9$

    $-\frac{9}{2}$

34. Find the number that completes the square for $x^2 + 16x$.

    $256$

    $16$

    $64$

    $8$

35. What value needs to be added to the expression $x^2 - 14x$ to complete the square?

    $196$

    $49$

    $-7$

    $14$

36. To complete the square for $x^2 + \frac{1}{2}x$, what term should be added?

    $\frac{1}{16}$

    $\frac{1}{4}$

    $\frac{1}{16}x$

    $\frac{1}{2}$

37. Identify the constant term that completes the square for $x^2 - \frac{2}{5}x$.

    $-\frac{1}{5}$

    $\frac{1}{25}$

    $\frac{4}{25}$

    $\frac{2}{25}$