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Answer :
Sure, let's answer each question one by one:
1. Which of the following polynomials has two terms?
- A binomial is a polynomial with two terms.
- Answer: A. Binomial
2. How many terms does the expression [tex]\(3x^2 + 5x - 7\)[/tex] have?
- This expression contains three terms: [tex]\(3x^2\)[/tex], [tex]\(5x\)[/tex], and [tex]\(-7\)[/tex].
- Answer: C. 3
3. What is the degree in the expression [tex]\(5x^2 + 9x - 7\)[/tex]?
- The degree of a polynomial is the highest power of the variable. Here, the highest power of [tex]\(x\)[/tex] is 2.
- Answer: B. 2
4. What is the numerical coefficient of [tex]\(35a^8\)[/tex]?
- The numerical coefficient is the number in front of the variable term, which is 35.
- Answer: D. 35
5. Which of the following polynomials has three terms?
- A trinomial is a polynomial with three terms.
- Answer: D. Trinomial
6. How many terms does [tex]\(3x^3 - x^2 + 8x - 2\)[/tex] have?
- This expression has four terms: [tex]\(3x^3\)[/tex], [tex]\(-x^2\)[/tex], [tex]\(8x\)[/tex], and [tex]\(-2\)[/tex].
- Answer: B. 4
7. Which of the following are symbols or letters that may take one or more than one value?
- Variables are symbols or letters that can represent different values.
- Answer: D. Variables
8. Which of the following polynomials has 1 term?
- A monomial is a polynomial with one term.
- Answer: B. Monomial
9. Which is the exponent in the term [tex]\(23a^4\)[/tex]?
- The exponent of [tex]\(a\)[/tex] is 4.
- Answer: D. 4
10. What is the numerical coefficient in the term [tex]\(ab^2\)[/tex]?
- Since there is no number written, the numerical coefficient is 1.
- Answer: C. 1
11. If [tex]\(b = -3\)[/tex], what would be the value of [tex]\(2b - 3b + 5\)[/tex]?
- Substitute [tex]\(b\)[/tex] with [tex]\(-3\)[/tex]: [tex]\(2(-3) - 3(-3) + 5 = -6 + 9 + 5 = 8\)[/tex].
- Answer: D. 8
12. What is the sum of [tex]\((9a + 5b^2)\)[/tex] and [tex]\((6a + 12b^2)\)[/tex]?
- Add the like terms: [tex]\((9a + 6a) + (5b^2 + 12b^2) = 15a + 17b^2\)[/tex].
- Answer: C. [tex]\(15a + 17b^2\)[/tex]
13. What is the sum of [tex]\((5m^2 - 7n^2)\)[/tex] and [tex]\((8m^2 + 6n^2)\)[/tex]?
- Add the like terms: [tex]\((5m^2 + 8m^2) + (-7n^2 + 6n^2) = 13m^2 - n^2\)[/tex].
- Answer: A. [tex]\(13m^2 - n^2\)[/tex]
14. What is the difference of [tex]\((-4xy)\)[/tex] and [tex]\((-5xy)\)[/tex]?
- Calculate [tex]\((-4xy) - (-5xy)\)[/tex]: [tex]\(xy\)[/tex].
- Answer: C. [tex]\(xy\)[/tex]
15. What would be the expression to be subtracted from [tex]\((abc + 6)\)[/tex] to obtain [tex]\((-10abc - 1)\)[/tex]?
- Solve [tex]\((abc + 6) - X = (-10abc - 1)\)[/tex] to find [tex]\(X\)[/tex]: [tex]\(X = abc + 6 + 10abc + 1 = 11abc + 7\)[/tex].
- Answer: B. [tex]\(-11abc - 7\)[/tex]
16. What would be the value of [tex]\(6b + 7b - 9\)[/tex], if [tex]\(b = 6\)[/tex]?
- Substitute [tex]\(b\)[/tex] with 6: [tex]\(6(6) + 7(6) - 9 = 36 + 42 - 9 = 69\)[/tex].
- Answer: C. 69
17. What is the sum of [tex]\((14a + 7b^2)\)[/tex] and [tex]\((8a + 16b^2)\)[/tex]?
- Add the like terms: [tex]\((14a + 8a) + (7b^2 + 16b^2) = 22a + 23b^2\)[/tex].
- Answer: D. [tex]\(22a + 23b^2\)[/tex]
18. What is the difference of [tex]\((12b^2)\)[/tex] and [tex]\((5b^2)\)[/tex]?
- Calculate [tex]\(12b^2 - 5b^2 = 7b^2\)[/tex].
- Answer: C. [tex]\(7b^2\)[/tex]
19. If [tex]\((20m^2 + n^2)\)[/tex] is subtracted from [tex]\((20m^2 - 19n^2)\)[/tex], what is the difference?
- Calculate the expression: [tex]\((20m^2 - 19n^2) - (20m^2 + n^2) = - 20n^2\)[/tex].
- Answer: A. [tex]\(-20n^2\)[/tex]
20. What is the difference if [tex]\((2x^2 + 3x + 4)\)[/tex] is subtracted from [tex]\((5x^2 - 7x - 10)\)[/tex]?
- Calculate: [tex]\((5x^2 - 7x - 10) - (2x^2 + 3x + 4) = 3x^2 - 10x - 14\)[/tex].
- Answer: C. [tex]\(3x^2 - 10x - 14\)[/tex]
Feel free to ask if you have any more questions!
1. Which of the following polynomials has two terms?
- A binomial is a polynomial with two terms.
- Answer: A. Binomial
2. How many terms does the expression [tex]\(3x^2 + 5x - 7\)[/tex] have?
- This expression contains three terms: [tex]\(3x^2\)[/tex], [tex]\(5x\)[/tex], and [tex]\(-7\)[/tex].
- Answer: C. 3
3. What is the degree in the expression [tex]\(5x^2 + 9x - 7\)[/tex]?
- The degree of a polynomial is the highest power of the variable. Here, the highest power of [tex]\(x\)[/tex] is 2.
- Answer: B. 2
4. What is the numerical coefficient of [tex]\(35a^8\)[/tex]?
- The numerical coefficient is the number in front of the variable term, which is 35.
- Answer: D. 35
5. Which of the following polynomials has three terms?
- A trinomial is a polynomial with three terms.
- Answer: D. Trinomial
6. How many terms does [tex]\(3x^3 - x^2 + 8x - 2\)[/tex] have?
- This expression has four terms: [tex]\(3x^3\)[/tex], [tex]\(-x^2\)[/tex], [tex]\(8x\)[/tex], and [tex]\(-2\)[/tex].
- Answer: B. 4
7. Which of the following are symbols or letters that may take one or more than one value?
- Variables are symbols or letters that can represent different values.
- Answer: D. Variables
8. Which of the following polynomials has 1 term?
- A monomial is a polynomial with one term.
- Answer: B. Monomial
9. Which is the exponent in the term [tex]\(23a^4\)[/tex]?
- The exponent of [tex]\(a\)[/tex] is 4.
- Answer: D. 4
10. What is the numerical coefficient in the term [tex]\(ab^2\)[/tex]?
- Since there is no number written, the numerical coefficient is 1.
- Answer: C. 1
11. If [tex]\(b = -3\)[/tex], what would be the value of [tex]\(2b - 3b + 5\)[/tex]?
- Substitute [tex]\(b\)[/tex] with [tex]\(-3\)[/tex]: [tex]\(2(-3) - 3(-3) + 5 = -6 + 9 + 5 = 8\)[/tex].
- Answer: D. 8
12. What is the sum of [tex]\((9a + 5b^2)\)[/tex] and [tex]\((6a + 12b^2)\)[/tex]?
- Add the like terms: [tex]\((9a + 6a) + (5b^2 + 12b^2) = 15a + 17b^2\)[/tex].
- Answer: C. [tex]\(15a + 17b^2\)[/tex]
13. What is the sum of [tex]\((5m^2 - 7n^2)\)[/tex] and [tex]\((8m^2 + 6n^2)\)[/tex]?
- Add the like terms: [tex]\((5m^2 + 8m^2) + (-7n^2 + 6n^2) = 13m^2 - n^2\)[/tex].
- Answer: A. [tex]\(13m^2 - n^2\)[/tex]
14. What is the difference of [tex]\((-4xy)\)[/tex] and [tex]\((-5xy)\)[/tex]?
- Calculate [tex]\((-4xy) - (-5xy)\)[/tex]: [tex]\(xy\)[/tex].
- Answer: C. [tex]\(xy\)[/tex]
15. What would be the expression to be subtracted from [tex]\((abc + 6)\)[/tex] to obtain [tex]\((-10abc - 1)\)[/tex]?
- Solve [tex]\((abc + 6) - X = (-10abc - 1)\)[/tex] to find [tex]\(X\)[/tex]: [tex]\(X = abc + 6 + 10abc + 1 = 11abc + 7\)[/tex].
- Answer: B. [tex]\(-11abc - 7\)[/tex]
16. What would be the value of [tex]\(6b + 7b - 9\)[/tex], if [tex]\(b = 6\)[/tex]?
- Substitute [tex]\(b\)[/tex] with 6: [tex]\(6(6) + 7(6) - 9 = 36 + 42 - 9 = 69\)[/tex].
- Answer: C. 69
17. What is the sum of [tex]\((14a + 7b^2)\)[/tex] and [tex]\((8a + 16b^2)\)[/tex]?
- Add the like terms: [tex]\((14a + 8a) + (7b^2 + 16b^2) = 22a + 23b^2\)[/tex].
- Answer: D. [tex]\(22a + 23b^2\)[/tex]
18. What is the difference of [tex]\((12b^2)\)[/tex] and [tex]\((5b^2)\)[/tex]?
- Calculate [tex]\(12b^2 - 5b^2 = 7b^2\)[/tex].
- Answer: C. [tex]\(7b^2\)[/tex]
19. If [tex]\((20m^2 + n^2)\)[/tex] is subtracted from [tex]\((20m^2 - 19n^2)\)[/tex], what is the difference?
- Calculate the expression: [tex]\((20m^2 - 19n^2) - (20m^2 + n^2) = - 20n^2\)[/tex].
- Answer: A. [tex]\(-20n^2\)[/tex]
20. What is the difference if [tex]\((2x^2 + 3x + 4)\)[/tex] is subtracted from [tex]\((5x^2 - 7x - 10)\)[/tex]?
- Calculate: [tex]\((5x^2 - 7x - 10) - (2x^2 + 3x + 4) = 3x^2 - 10x - 14\)[/tex].
- Answer: C. [tex]\(3x^2 - 10x - 14\)[/tex]
Feel free to ask if you have any more questions!
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