Simplify Polynomials - International Brotherhood of Electrical Workers Exam IBEW

1. What is the simplified form of $9a-14a$?

   $-5a$. Subtract the coefficients of the like terms with variable $a$.

2. What is the coefficient of the term $-7x^3y$?

   $-7$. The coefficient is the numerical factor preceding the variables in a term.

3. What is the constant term in the expression $4x^2-9x+12$?

   $12$. The constant term lacks variables and remains unchanged in the expression.

4. What is the simplified form of $7x+3x$?

   $10x$. Add the coefficients of the like terms sharing the variable $x$.

5. What is the simplified form of $-5x^2+2x-3-4x^2+7x+9$?

   $-9x^2+9x+6$. Group like terms for $x^2$, $x$, and constants, then combine their coefficients.

6. What is the simplified form of $4x^2+3x-7x^2+5x$?

   $-3x^2+8x$. Group and combine coefficients for $x^2$ terms and $x$ terms separately.

7. What is the simplified form of $x^2+x+x^2-x$?

   $2x^2$. Combine $x^2$ terms and cancel the opposing $x$ terms.

8. What is the simplified form of $0.6x^2-1.1x^2+0.5x^2$?

   $0x^2$. Add and subtract decimal coefficients for the $x^2$ terms, resulting in zero.

9. What is the simplified form of $(x^2-3x+2)+(5x^2+x-7)$?

   $6x^2-2x-5$. Remove parentheses and combine like terms for $x^2$, $x$, and constants.

10. What is the simplified form of $-x^3+4x^3-2x^3+x^3$?

    $2x^3$. Add and subtract coefficients for the like $x^3$ terms.

11. What is the simplified form of $4(x^2-2x+1)-x^2+3x$?

    $3x^2-5x+4$. Distribute the 4, then combine like terms for $x^2$, $x$, and constants.

12. Identify the simplified form of $-3(2x^2-x+4)+x^2-5$.

    $-5x^2+3x-17$. Distribute the -3, then combine like terms for $x^2$, $x$, and constants.

13. What is the simplified form of $2a^2b+7a^2b-3a^2b$?

    $6a^2b$. Add and subtract coefficients for terms sharing $a^2b$.

14. What is the simplified form of $2x^2y-5xy^2+3x^2y+7xy^2$?

    $5x^2y+2xy^2$. Group and combine coefficients for $x^2y$ terms and $xy^2$ terms separately.

15. What is the simplified form of $6m^3-2m^3+9m^3$?

    $13m^3$. Combine coefficients of like terms with $m^3$ by adding and subtracting.

16. What is the simplified form of $5y^2+12y^2-3y^2$?

    $14y^2$. Combine coefficients by adding and subtracting for terms with $y^2$.

17. Which terms are like terms: $3x^2$, $-5x^2$, $3x$, $3x^2y$?

    $3x^2$ and $-5x^2$. These terms share the variable $x$ raised to the power of 2, making them combinable.

18. What is the simplified form of $3a^2-2ab+5b^2+a^2+7ab-3b^2$?

    $4a^2+5ab+2b^2$. Group and combine coefficients for $a^2$, $ab$, and $b^2$ terms separately.

19. What is the definition of like terms in a polynomial?

    Terms with identical variable parts (same variables to same powers). Like terms share the same variables raised to the same powers, enabling combination of their coefficients when simplifying polynomials.

20. What is the simplified form of $3(x+4)+2x$?

    $5x+12$. Distribute the 3, then combine like terms for $x$ and constants.

21. What is the simplified form of $-2(3x-5)+x$?

    $-5x+10$. Distribute the -2, then combine the resulting $x$ terms.

22. Find the simplified form of $-(-4x+7)+2x-3$.

    $6x-10$. Distribute the negative sign, then combine $x$ terms and constants separately.

23. What is the simplified form of $8p-3q+2p+9q$?

    $10p+6q$. Combine coefficients for $p$ terms and $q$ terms independently.

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