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6-1 Additional Practice Adding and Subtracting Polynomials What is the name of each polynomial, based on the degree and the number of terms? 1. -4x^2y 2 3x^4-2x^3+5x^2+6x-12 3. x^2+5x-4 Write each polynomial in standard form. 4 3x^2-5x-4+x^3 5 -7+2x-x^5+4x^4+2x^3 6. 9-x^2+5x Combine like terms and write each expression in standard form. 9. x^2-5+2x+x^2 7 -5y+3y^2+2y-2y^2-9 8 -2x^2+x+5x^3+4x+2x^2 Add or subtract. Write each answer in standard form. 10 (4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12) 11 (x^4-3x^3+5x^2+x-4)-(x^3-4x^2-11x+10)

Pergunta

6-1 Additional Practice
Adding and Subtracting Polynomials
What is the name of each polynomial, based on the degree and the number
of terms?
1. -4x^2y
2 3x^4-2x^3+5x^2+6x-12
3. x^2+5x-4
Write each polynomial in standard form.
4 3x^2-5x-4+x^3
5 -7+2x-x^5+4x^4+2x^3
6. 9-x^2+5x
Combine like terms and write each expression in standard form.
9. x^2-5+2x+x^2
7 -5y+3y^2+2y-2y^2-9
8
-2x^2+x+5x^3+4x+2x^2
Add or subtract. Write each answer in standard form.
10
(4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12)
11
(x^4-3x^3+5x^2+x-4)-(x^3-4x^2-11x+10)

6-1 Additional Practice Adding and Subtracting Polynomials What is the name of each polynomial, based on the degree and the number of terms? 1. -4x^2y 2 3x^4-2x^3+5x^2+6x-12 3. x^2+5x-4 Write each polynomial in standard form. 4 3x^2-5x-4+x^3 5 -7+2x-x^5+4x^4+2x^3 6. 9-x^2+5x Combine like terms and write each expression in standard form. 9. x^2-5+2x+x^2 7 -5y+3y^2+2y-2y^2-9 8 -2x^2+x+5x^3+4x+2x^2 Add or subtract. Write each answer in standard form. 10 (4x^3-5x^2+3x-8)+(2x^3-2x^2+6x+12) 11 (x^4-3x^3+5x^2+x-4)-(x^3-4x^2-11x+10)

Solução

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LorenaMestre · Tutor por 5 anos

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1. The polynomial $-4x^{2}y$ is a monomial because it has only one term. It is of degree 3 because the highest power of the variable is 3.<br /><br />2. The polynomial $3x^{4}-2x^{3}+5x^{2}+6x-12$ is a polynomial of degree 4 because the highest power of the variable is 4. It has 5 terms, so it is a quintic polynomial.<br /><br />3. The polynomial $x^{2}+5x-4$ is a trinomial because it has three terms. It is of degree 2 because the highest power of the variable is 2.<br /><br />4. To write the polynomial $3x^{2}-5x-4+x^{3}$ in standard form, we need to arrange the terms in descending order of their degrees. So, the standard form is $x^{3}+3x^{2}-5x-4$.<br /><br />5. To write the polynomial $-7+2x-x^{5}+4x^{4}+2x^{3}$ in standard form, we need to arrange the terms in descending order of their degrees. So, the standard form is $-x^{5}+4x^{4}+2x^{3}+2x-7$.<br /><br />6. To write the polynomial $9-x^{2}+5x$ in standard form, we need to arrange the terms in descending order of their degrees. So, the standard form is $-x^{2}+5x+9$.<br /><br />7. To combine like terms and write the expression $-5y+3y^{2}+2y-2y^{2}-9$ in standard form, we need to combine the like terms. So, the standard form is $y^{2}-3y-9$.<br /><br />8. To combine like terms and write the expression $-2x^{2}+x+5x^{3}+4x+2x^{2}$ in standard form, we need to combine the like terms. So, the standard form is $5x^{3}+5x$.<br /><br />9. To combine like terms and write the expression $x^{2}-5+2x+x^{2}$ in standard form, we need to combine the like terms. So, the standard form is $2x^{2}+2x-5$.<br /><br />10. To add the polynomials $(4x^{3}-5x^{2}+3x-8)+(2x^{3}-2x^{2}+6x+12)$, we need to add the like terms. So, the sum is $6x^{3}-7x^{2}+9x+4$.<br /><br />11. To subtract the polynomials $(x^{4}-3x^{3}+5x^{2}+x-4)-(x^{3}-4x^{2}-11x+10)$, we need to subtract the like terms. So, the difference is $x^{4}-4x^{3}+9x^{2}+12x-14$.
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