5. POLY Review for Test WS Name $$ \qquad $$ Hour $$ \qquad $$ 7-6 Polynomials Write each polynomial in standard form and give the leading coefficient. 1. $$ 4 r^{2}+2 r^{6}-3 r $$ 2. $$ y^{2}+7-8 y^{3}+2 y $$ 3. $$ -12 t^{3}-4 t+t^{4} $$ 4. $$ n+3+3 n^{2} $$ 5. $$ 2+3 x^{3} $$ 6. $$ -3 a^{2}+16+a^{7}+a $$ Classify each polynomial according to its degree and number of terms. 7. $$ 2 x^{3}+5 x-4 $$ 8. $$ 5 b^{2} $$ 9. $$ 6 p^{2}+3 p-p^{4}+2 p^{3} $$ 10. $$ x^{2}+12-x $$ 11. $$ -2 x^{3}-5+x-2 x^{7} $$ 12. $$ 5-6 b^{2}+b-4 b^{4} $$ 7-7 Adding and Subtracting Polynomials Add or subtract. 14. $$ \left(10 m^{3}+4 m^{2}\right)+\left(7 m^{2}+3 m\right) $$ 15. $$ \left(3 t^{2}-2 t\right)+\left(9 t^{2}+4 t-6\right) $$ 16. $$ \left(12 d^{6}-3 d^{2}\right)+\left(2 d^{4}+1\right) $$ 17. $$ \left(6 y^{3}+4 y^{2}\right)-\left(2 y^{2}+3 y\right) $$ 18. $$ \left(7 n^{2}-3 n\right)-\left(5 n^{2}+5 n\right) $$ 19. $$ \left(b^{2}-10\right)-\left(-5 b^{3}+4 b\right) $$

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Let's go through each part of the problem step by step.

### 7-6 Polynomials

**1. Write each polynomial in standard form and give the leading coefficient.**

1. $$ 4 r^{2}+2 r^{6}-3 r $$

- Standard form: $$ 2 r^{6} + 4 r^{2} - 3 r $$
   - Leading coefficient: $$ 2 $$

2. $$ y^{2}+7-8 y^{3}+2 y $$

- Standard form: $$ -8 y^{3} + y^{2} + 2 y + 7 $$
   - Leading coefficient: $$ -8 $$

3. $$ -12 t^{3}-4 t+t^{4} $$

- Standard form: $$ t^{4} - 12 t^{3} - 4 t $$
   - Leading coefficient: $$ 1 $$

4. $$ n+3+3 n^{2} $$

- Standard form: $$ 3 n^{2} + n + 3 $$
   - Leading coefficient: $$ 3 $$

5. $$ 2+3 x^{3} $$

- Standard form: $$ 3 x^{3} + 2 $$
   - Leading coefficient: $$ 3 $$

6. $$ -3 a^{2}+16+a^{7}+a $$

- Standard form: $$ a^{7} - 3 a^{2} + a + 16 $$
   - Leading coefficient: $$ 1 $$

**Classify each polynomial according to its degree and number of terms.**

7. $$ 2 x^{3}+5 x-4 $$

- Degree: $$ 3 $$
   - Number of terms: $$ 3 $$ (trinomial)

8. $$ 5 b^{2} $$

- Degree: $$ 2 $$
   - Number of terms: $$ 1 $$ (monomial)

9. $$ 6 p^{2}+3 p-p^{4}+2 p^{3} $$

- Degree: $$ 4 $$
   - Number of terms: $$ 4 $$ (quadrinomial)

10. $$ x^{2}+12-x $$

- Degree: $$ 2 $$
    - Number of terms: $$ 3 $$ (trinomial)

11. $$ -2 x^{3}-5+x-2 x^{7} $$

- Degree: $$ 7 $$
    - Number of terms: $$ 4 $$ (quadrinomial)

12. $$ 5-6 b^{2}+b-4 b^{4} $$

- Degree: $$ 4 $$
    - Number of terms: $$ 4 $$ (quadrinomial)

### 7-7 Adding and Subtracting Polynomials

**Add or subtract.**

14. $$ \left(10 m^{3}+4 m^{2}\right)+\left(7 m^{2}+3 m\right) $$

- Result: $$ 10 m^{3} + 11 m^{2} + 3 m $$

15. $$ \left(3 t^{2}-2 t\right)+\left(9 t^{2}+4 t-6\right) $$

- Result: $$ 12 t^{2} + 2 t - 6 $$

16. $$ \left(12 d^{6}-3 d^{2}\right)+\left(2 d^{4}+1\right) $$

- Result: $$ 12 d^{6} + 2 d^{4} - 3 d^{2} + 1 $$

17. $$ \left(6 y^{3}+4 y^{2}\right)-\left(2 y^{2}+3 y\right) $$

- Result: $$ 6 y^{3} + 2 y^{2} - 3 y $$

18. $$ \left(7 n^{2}-3 n\right)-\left(5 n^{2}+5 n\right) $$

- Result: $$ 2 n^{2} - 8 n $$

19. $$ \left(b^{2}-10\right)-\left(-5 b^{3}+4 b\right) $$

- Result: $$ 5 b^{3} + b^{2} - 10 $$

This completes the review for the test. If you have any specific questions or need further assistance, feel free to ask!
**7-6 Polynomials** 1. $$ 4 r^{2}+2 r^{6}-3 r $$ - Standard form: $$ 2 r^{6} + 4 r^{2} - 3 r $$ - Leading coefficient: $$ 2 $$ 2. $$ y^{2}+7-8 y^{3}+2 y $$ - Standard form: $$ -8 y^{3} + y^{2} + 2 y + 7 $$ - Leading coefficient: $$ -8 $$ 3. $$ -12 t^{3}-4 t+t^{4} $$ - Standard form: $$ t^{4} - 12 t^{3} - 4 t $$ - Leading coefficient: $$ 1 $$ 4. $$ n+3+3 n^{2} $$ - Standard form: $$ 3 n^{2} + n + 3 $$ - Leading coefficient: $$ 3 $$ 5. $$ 2+3 x^{3} $$ - Standard form: $$ 3 x^{3} + 2 $$ - Leading coefficient: $$ 3 $$ 6. $$ -3 a^{2}+16+a^{7}+a $$ - Standard form: $$ a^{7} - 3 a^{2} + a + 16 $$ - Leading coefficient: $$ 1 $$ **Classification:** 7. $$ 2 x^{3}+5 x-4 $$ - Degree: $$ 3 $$ - Number of terms: $$ 3 $$ (trinomial) 8. $$ 5 b^{2} $$ - Degree: $$ 2 $$ - Number of terms: $$ 1 $$ (monomial) 9. $$ 6 p^{2}+3 p-p^{4}+2 p^{3} $$ - Degree: $$ 4 $$ - Number of terms: $$ 4 $$ (quadrinomial) 10. $$ x^{2}+12-x $$ - Degree: $$ 2 $$ - Number of terms: $$ 3 $$ (trinomial) 11. $$ -2 x^{3}-5+x-2 x^{7} $$ - Degree: $$ 7 $$ - Number of terms: $$ 4 $$ (quadrinomial) 12. $$ 5-6 b^{2}+b-4 b^{4} $$ - Degree: $$ 4 $$ - Number of terms: $$ 4 $$ (quadrinomial) **7-7 Adding and Subtracting Polynomials** 14. $$ \left(10 m^{3}+4 m^{2}\right)+\left(7 m^{2}+3 m\right) $$ - Result: $$ 10 m^{3} + 11 m^{2} + 3 m $$ 15. $$ \left(3 t^{2}-2 t\right)+\left(9 t^{2}+4 t-6\right) $$ - Result: $$ 12 t^{2} + 2 t - 6 $$ 16. $$ \left(12 d^{6}-3 d^{2}\right)+\left(2 d^{4}+1\right) $$ - Result: $$ 12 d^{6} + 2 d^{4} - 3 d^{2} + 1 $$ 17. $$ \left(6 y^{3}+4 y^{2}\right)-\left(2 y^{2}+3 y\right) $$ - Result: $$ 6 y^{3} + 2 y^{2} - 3 y $$ 18. $$ \left(7 n^{2}-3 n\right)-\left(5 n^{2}+5 n\right) $$ - Result: $$ 2 n^{2} - 8 n $$ 19. $$ \left(b^{2}-10\right)-\left(-5 b^{3}+4 b\right) $$ - Result: $$ 5 b^{3} + b^{2} - 10 $$ **Summary:** - **7-6 Polynomials:** Converted each polynomial to standard form and identified the leading coefficient. Classified each polynomial based on its degree and number of terms. - **7-7 Adding and Subtracting Polynomials:** Performed addition and subtraction of polynomials and provided the results. If you have any specific questions or need further assistance, feel free to ask!

POLY Review for Test WS

Name
Hour

7-6 Polynomials
Write each polynomial in standard form and give the leading coefficient.

Classify each polynomial according to its degree and number of terms.
7.
8.
9.
10.
11.
12.

7-7 Adding and Subtracting Polynomials
Add or subtract.
14.
15.
16.
17.
18.
19.

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7-6 Polynomials

7-7 Adding and Subtracting Polynomials

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