Multiple Choice

1. What is the classification of the polynomial $5x^3 - 2x + 1$ based on the number of terms?

   Binomial

   Polynomial of four terms

   Trinomial

   Monomial

2. Determine the degree of the monomial $7a^2b^5$.

   5

   2

   7

3. Which of the following polynomials is a binomial of degree 4?

   $4x^5 + 9$

   $10x^3y^2$

   $x^4 - 16$

   $3x^4 - 5x^3 + 1$

4. Classify the expression $-12p^7$ by its number of terms.

   Trinomial

   Monomial

   Binomial

   Polynomial

5. What is the degree of the polynomial $3x^2y - 5x^4 + 10$?

   3

   10

   2

   4

6. Find the Greatest Common Factor (GCF) of the terms $18x^3y^2$ and $45x^2y^4$.

   $3x^2y^2$

   $9x^2y^2$

   $9x^3y^4$

   $18x^2y^2$

7. What is the GCF of the three monomials: $14a^5$, $21a^3$, and $7a^4$?

   $7a^3$

   $7a$

   $7a^5$

   $14a^3$

8. Determine the GCF of $24m^2n$ and $36mn^3p$.

   $6mn$

   $12mn$

   $12mn^3$

   $12m^2n^3$

9. Find the GCF of the terms $50x^6$ and $75x^4$.

   $25x^6$

   $5x^4$

   $25x^4$

   $25x^2$

10. What is the greatest common monomial factor of the expression $4p^2q^3 + 12p^3q^2 - 8p^4q$?

    $8p^2q$

    $4pq$

    $4p^4q^3$

    $4p^2q$

11. Factor the expression $15x^2 - 20x$ completely using the GCF.

    $5x(3x - 4x)$

    $5x(3x - 4)$

    $5(3x^2 - 4x)$

    $5x^2(3 - 4/x)$

12. Factor the polynomial $9y^5 + 6y^3 - 3y^2$ using the GCF.

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

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

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

13. When $42a^3b^2 - 14a^2b^3$ is factored completely, what is the binomial factor remaining?

    $(3a - b^2)$

    $(3a - b)$

    $(3a - 1)$

    $(3a^3b^2 - b)$

14. Factor $-16r^4 + 8r^3$ by factoring out a GCF of $-8r^3$.

    $-8r^3(2r - 1)$

    $8r^3(2r + 1)$

    $-8r^3(2r + 1)$

15. Identify the correct factored form of $10m^3n^2 + 5m^2n$.

    $10m^2n(mn + 1/2)$

    $5m^2n(2mn + 1)$

    $5mn(2m^2n + m)$

    $5m^2n(2mn)$

16. Factor the expression $ax + ay + 5x + 5y$ by grouping.

    $5a(x+y)$

    $a(x + y) + 5(x + y)$

    $(a+5)(x+5y)$

    $(a + 5)(x + y)$

17. When factoring $x^3 + 2x^2 + 3x + 6$ by grouping, what is the common binomial factor after the first step?

    $(x^2 + 3)$

    $(x + 2)$

    $(3x + 6)$

18. Factor the polynomial $2xy + 6x - y - 3$ completely by grouping.

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

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

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

19. Factor $4m^3 - 8m^2 + 3m - 6$ completely.

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

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

    $(4m^2 - 1)(m + 6)$

20. Which of the following is a factor of $p^2r - pr^2 + 5p - 5r$?

    $(p + r)$

    $(p - r)$

    $(p^2 - r)$

    $(pr + 5)$

21. Factor the expression $3ab - 21a + 5b - 35$ by grouping.

    $3a(b-7) + 5(b+7)$

    $(3a - 5)(b - 7)$

    $(3a + 5)(b + 7)$

    $(3a + 5)(b - 7)$

22. Factor $x^3 - x^2 - 9x + 9$ completely using grouping.

    $(x^2 + 9)(x - 1)$

    $(x^2 - 9)(x^2 + 1)$

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

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

23. What is the result of factoring $a^2b - a^2c - 4b + 4c$?

    $(b - c)(a - 2)$

    $(a^2 - 4)(b + c)$

    $(a^2 + 4)(b - c)$

    $(b - c)(a - 2)(a + 2)$

24. When factoring $6x^3 + 9x^2 - 2x - 3$ by grouping, which expression represents the factors?

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

    $(6x^2 - 1)(x + 3)$

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

25. Identify one of the factors of the polynomial $5x^2y - 10x^2 + 3y - 6$.

    $(10x^2 + 6)$

    $(5x^2 - 3)$

    $(5x^2 + 3)$

    $(y + 2)$

26. Factor the polynomial $3x + 3y + ax + ay$ completely using the grouping method.

    $(3+a)(x+ay)$

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

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

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

27. Factor the expression $2ab + 6a + b + 3$.

    $6a(b+1)$

    $2a(b+3) + (b+3)$

    $(2a+3)(b+1)$

    $(2a+1)(b+3)$

28. Factor $5x - 5y + ax - ay$ completely.

    $5(x-y) + a(x-y)$

    $(5+a)(x-y)$

    $(5+a)(x+y)$

    $(5-a)(x+y)$

29. Factor the polynomial $x^3 + 2x^2 + 5x + 10$ using the grouping method.

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

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

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

    $(x^2+1)(x+10)$

30. Factor the expression $4m^2 - 8m - 3m + 6$.

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

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

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

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

31. Factor the polynomial $a^2b + 3a^2 + 2b + 6$.

    $(a^2+3)(b+2)$

    $(a^2+b)(3a^2+6)$

    $(a^2+2)(b+3)$

    $a^2(b+3) + 2(b+3)$

32. Factor the expression $12y^2 - 4y + 9xy - 3x$.

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

    $(12y+3x)(y-1)$

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

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

33. Completely factor the polynomial $10ac - 15ad - 8bc + 12bd$.

    $(5a+4b)(2c-3d)$

    $(5a-4b)(2c-3d)$

    $(5a-4b)(2c+3d)$

    $5a(2c-3d) + 4b(-2c+3d)$

34. Factor the polynomial $x^2y + x^2 + 5y + 5$.

    $(x^2y+5)(1+y)$

    $(x^2+5)(y+1)$

    $x^2(y+1) + 5(y+1)$

    $(x^2+1)(y+5)$

35. Factor $x^3 + 4x^2 + x + 4$.

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

    $(x^2+1)(x+4)$

    $(x+4)(x^2-1)$

    $(x^2+4)(x+1)$

36. Factor $6p^3 + 9p^2 + 2p + 3$ completely.

    $(3p^2+1)(2p+3)$

    $(6p^2+1)(p+3)$

    $3p^2(2p+3) + 2p+3$

    $(3p^2+3)(2p+1)$

37. Factor the expression $3kn + 15k - n - 5$.

    $(3k+1)(n-5)$

    $(3k-1)(n+5)$

    $(3k-5)(n+1)$

    $3k(n+5) - (n+5)$

38. Factor $2x^3 - 4x^2 + 6x - 12$ completely.

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

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

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

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

39. Factor the polynomial $-7y + 14 + xy - 2x$.

    $x(y-2) + 7(2-y)$

    $(x-7)(y-2)$

    $(x-7)(2-y)$

    $(x+7)(y+2)$

40. Factor $15 - 5x + 3y - xy$.

    $(5+y)(x-3)$

    $(5+y)(3-x)$

    $5(3-x) + y(3-x)$

    $(15+y)(1-x)$

41. Factor the polynomial $a^4 + a^2c + 5a^2 + 5c$.

    $(a^4+5)(a^2+c)$

    $(a^2+5)(a^2+c)$

    $(a^2+c)(a^2+1)$

    $a^2(a^2+c) + 5(a^2+c)$

42. Factor $14xy - 21x - 10y + 15$.

    $(7x-5)(2y-3)$

    $(7x+5)(2y+3)$

    $(14x-1)(y+15)$

    $7x(2y-3) + 5(-2y+3)$

43. Factor $r^2s - 4r^2 - rs + 4r$ completely.

    $r(r-1)(s-4)$

    $r^2(s-4) - r(s-4)$

    $r(r+1)(s-4)$

    $(r^2-r)(s-4)$

44. Factor $2x^3 - 6x^2y + 4x - 12y$ completely.

    $(x^2+2)(2x-12y)$

    $2(x^2-2)(x+3y)$

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

    $2(x^2+2)(x-3y)$

45. Factor $5ax + 5ay + bx + by$.

    $5a(x+y) + b(x+y)$

    $(5x+5y)(a+b)$

    $(5a+x)(b+y)$

    $(5a+b)(x+y)$