Terms, Factors, & Coefficients - Algebra 2

1. What is the leading coefficient of the polynomial $6x^4-2x+3$?

   $6$. The coefficient of the highest degree term.

2. What is the coefficient of $x^2$ in the expanded form of $x(x+2)$?

   $1$. After expanding: $x^2 + 2x$, coefficient is $1$.

3. Identify the numerical coefficient in the term $-\frac{3}{5}ab^2$.

   $-\frac{3}{5}$. The fraction multiplying the variable part.

4. What does it mean for an expression to be a sum of terms?

   It is written using addition/subtraction between terms. Each term is connected by addition or subtraction.

5. Identify the constant term in the polynomial $-8x^2+0x+11$.

   $11$. The term with no variables, coefficient of $x^0$.

6. Identify the factors of the expression $x^2+5x$ as a product.

   $x(x+5)$. Common factor $x$ factored out.

7. Identify the top-level terms in the expression $4x-(2x-7)$.

   $4x$ and $-(2x-7)$. The subtraction creates two main terms.

8. What is the coefficient of $x^2$ in the expression $3-2x^2+9x^5$?

   $-2$. The number multiplying $x^2$ in that term.

9. Identify the coefficient of $x$ in the expression $x(x+2)$ when viewed as $x\text{ times }(x+2)$.

   $1$. The coefficient of $x$ when treating this as multiplication.

10. Which expression shows $-6x^2y$ as a product of a coefficient and variable factors?

    $-6 \times x^2 \times y$. Shows coefficient separated from variable factors.

11. What is the coefficient of $x^3$ in the expression $-x^3+2x^2-x+8$?

    $-1$. The negative sign indicates coefficient $-1$.

12. What is the coefficient of $x$ in the expanded form of $x(x+2)$?

    $2$. After expanding: $x^2 + 2x$, coefficient is $2$.

13. Identify the factors of the term $4x^2y$ written as a product of three factors.

    $4 \times x^2 \times y$. Breaking down into coefficient, $x^2$, and $y$.

14. What is the greatest common factor of the terms $6x^2$ and $9x$?

    $3x$. Factor out the highest power common to both terms.

15. What is a factor in an algebraic expression?

    A quantity multiplied by other quantities. Factors are multiplied together to form a product.

16. Identify the number of terms in the expression $7(x+1)$.

    $1$. The parentheses make this one complete term.

17. What is the implied coefficient of $x$ in the term $x$?

    $1$. When no coefficient is written, it equals $1$.

18. What is a coefficient of a variable term?

    The numerical factor multiplying the variable part. The number multiplying the variables in a term.

19. Identify the numerical coefficient in the term $-\frac{3}{5}ab^2$.

    $-\frac{3}{5}$. The fraction multiplying the variable part.

20. What is the implied coefficient of $-x$ in the term $-x$?

    $-1$. The negative sign indicates coefficient $-1$.

21. Identify the coefficient of $(x-4)$ in the expression $3(x-4)+2$.

    $3$. The number multiplying the parenthetical expression.

22. What is the leading term of the polynomial $-3x^5+4x^2-1$?

    $-3x^5$. The term with the highest degree.

23. Identify the coefficient of $x^2y$ in the term $9x^2y$.

    $9$. The number multiplying the entire variable part.

24. Identify the factors of the term $-14x^3$.

    $-14$ and $x^3$. The coefficient $-14$ and variable part $x^3$.

25. Identify the coefficient of $x^2y^3$ in the term $x^2y^3$.

    $1$. When no number is shown, coefficient is $1$.

26. Identify the coefficient of $x^2$ in the expression $-4x^2+9x-1$.

    $-4$. The number multiplying $x^2$ in the term.

27. Identify the factors in the term $-2(x+3)$.

    $-2$ and $(x+3)$. The coefficient and the parenthetical expression.

28. Identify the constant term in the simplified form of $-(x-5)$.

    $5$. From distributing: $-x + 5$, the constant is $5$.

29. Identify the coefficient of $x$ in the expression $-9x+4$.

    $-9$. The number directly multiplying $x$.

30. Which part of $8(x-1)(x+2)$ is the coefficient of the product $(x-1)(x+2)$?

    $8$. The number multiplying the entire parenthetical expression.

31. Identify the coefficient of $x$ in the expression $-(x-5)$ after simplifying.

    $-1$. Distribute the negative: $-x + 5$, so coefficient is $-1$.

32. What is the degree of the monomial $7x^3y^2$?

    $5$. Add the exponents: $3 + 2 = 5$.

33. Identify the factors of the expression $x^2-9$ as a product.

    $(x-3)(x+3)$. Factored form of the difference of squares.

34. Identify the coefficient of $ab$ in the expression $-7ab+3a-2b$.

    $-7$. The number multiplying both variables $a$ and $b$.

35. Identify the terms in the expression $3x^2-5x+7$.

    $3x^2$, $-5x$, $7$. Terms are separated by plus and minus signs.

36. Identify the variable factors in the term $6x^2y^3$.

    $x^2$ and $y^3$. The parts containing variables with their exponents.

37. Identify the terms in the expression $2(a-3)+5$.

    $2(a-3)$ and $5$. Each part separated by addition at the top level.

38. Identify the coefficient of $x^2$ in the expression $x^2-6x+1$.

    $1$. When no number is shown, the coefficient is $1$.

39. What is a constant term in an expression?

    A term with no variables. It contains only numbers, no variable parts.

40. Identify the coefficient of $x^0$ in the polynomial $4x^2-3x+9$.

    $9$. The constant term is the coefficient of $x^0$.

41. Identify the coefficient of $x$ in the expression $\frac{1}{2}x-3$.

    $\frac{1}{2}$. The fraction multiplying the variable $x$.

42. Identify the coefficient of $x^2y^3$ in the term $-x^2y^3$.

    $-1$. The negative sign indicates coefficient $-1$.

43. Identify the constant factor in the term $\frac{7}{3}x^4$.

    $\frac{7}{3}$. The fractional coefficient of the variable part.

44. Identify the number of terms in the expression $5x^2y-2y+9$.

    $3$. Count parts separated by plus or minus signs.

45. Identify the constant factor in the term $15mn$.

    $15$. The numerical part of the term.

46. Identify the constant term in the expression $12-3x+2x^2$.

    $12$. The term with no variables attached.

47. Identify the terms in the expression $-5(a+b)+2$.

    $-5(a+b)$ and $2$. Two parts separated by addition.

48. Identify the coefficient of $y$ in the expression $4x+3y-2$.

    $3$. The number multiplying the variable $y$.

49. What is a term in an algebraic expression?

    A part separated by $+$ or $-$ at the top level. Terms are separated by addition or subtraction operations.

50. Identify the variable part of the term $-12x^3y$.

    $x^3y$. All the variable parts with their exponents.

51. What is the meaning of the coefficient in the term $kx$ when $k$ is a constant?

    $k$ is the number multiplying $x$. It represents how many times $x$ is counted.

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