Hello, I need some clarification for my answers, thanks!
1. What is the degree of the monomial?
A. 5
B. 12***
C. 17
D. 60
2. What is the degree of the monomial?
-2
A. -2
B. -3
C. 0***
D. -1
What is the sum or difference?
3.
2x^4 - 8x^4
A. -6x^8
B. -6x^4***
C. -16x^4
D. -16x^8
What is the sum or difference?
4.
5y^4 - 9y^4
A. -45y^4
B. 14y^4
C. -4y^4***
D. -4y^8
5. Write the polynomial in standard form, then name the polynomial based on its degree and its number of terms.
2 - 5x^3 + 6x
A. 2 - 5x^3 + 6x; not a polynomial
B. -5x^3 + 6x +2;cubic-trinomial***
C. -5x^3 + 6x + 2;quadratic-trinomial
D. 6x - 5x^3 + 2;fourth-degree-trinomial(X) (No such term.)
These are what I have so far. I will update my post as I answer the questions.
1. The degree of a monomial is the sum of the exponents of its variables. Looking at the options given, if the monomial has a degree of 5, it would have at least one variable with an exponent of 5. Similarly, if the degree is 17, there would be at least one variable with an exponent of 17. The same goes for a degree of 60.
Based on this, the only option left is B. 12, as it represents the degree of the monomial.
2. Similar to the previous question, the degree of a monomial is the sum of the exponents of its variables. In this case, the monomial is -2, which can be written as -2x^0. Since the exponent of x is 0, the degree of the monomial is 0.
Therefore, the correct answer is C. 0.
3. When adding or subtracting monomials with the same variable(s), you only need to combine the coefficients. In this case, the monomials are 2x^4 and -8x^4. Adding or subtracting the coefficients gives us:
2x^4 - 8x^4 = -6x^4.
So, the correct answer is B. -6x^4.
4. Following the same logic as the previous question, the monomials in question are 5y^4 and -9y^4. Adding or subtracting the coefficients gives us:
5y^4 - 9y^4 = -4y^4.
Thus, the correct answer is C. -4y^4.
5. To write a polynomial in standard form, you arrange the terms in decreasing order of their exponents. In this case, the polynomial is 2 - 5x^3 + 6x.
Now, let's categorize it based on the degree and the number of terms:
- The highest exponent is x^3, so it's a cubic polynomial.
- The polynomial has three terms: 2, -5x^3, and 6x, so it's a trinomial.
Putting it together, the correct answer is B. -5x^3 + 6x + 2; cubic-trinomial.
Hope this clarifies your answers! Let me know if you have any further questions.
#1 has no monomial...
the rest look good.
Sweet! I apologize, the problem is here for one.
5x^12
then your are right here, too.
good work