Identify each polynomial below as a MONOMIAL, BINOMIAL, TRINOMIAL or OTHER.

___________________ 1. 3x3 + 8x

2 –x

___________________ 2. a2b

3(x + y) + 3ab(x + y)

___________________ 3. 7ab2cd

8efg

Write the degree of each polynomial in the blank.

______ 4. 3a – 4 a2 – 3a

3

______ 5. x2y

3 + 3xy

______ 6. 7ab2cd

8efg

9-13. Multiply the polynomials in each problem.

________________________ 9. 4x7(3x

2 – x – 7)

________________________ 10. (7y + 1)(3y – 1)

________________________ 11. (2x2 + 3)( 2x

2 – 3) Recall: these are CONJUGATES & the product will be a difference of perfect squares.

________________________ 12. (7a + 2)(7a + 2) Recall: this will result in a PST – a Perfect Square Trinomial.

___________________________________13. (2a + 3)(a2 – 8a – 3)

___________________________________14. Expand: (x + y)3

Careful! Some students confuse “cubing a binomial” with “factoring the sum of cubes”

___________________________________15. Factor: x3 + y

3

___________________________________16. Expand: (2a + 3)4

Algebra 2 w/ Trig

Semester Exam

Review 9 Polynomials

NAME ___________________________

Date :

Hint: the DEGREE of any one term is the sum of the exponents on the variables

The DEGREE of an entire polynomial is the highest degree found in any of the terms.

Hint: terms are separated only by + or – signs. A product or quotient is a single term.

Hints: may always use DISTRIBUTIVE PROPERTY repeatedly. (FOIL is a special case of Dist. Prop.)

Hint: use Binomial Theorem and Pascal’s Triangle if you are raising a binomial to a power.

Identify each polynomial below as a MONOMIAL, BINOMIAL, TRINOMIAL or OTHER.

___________________ 1. 3x3 + 8x

2 –x

___________________ 2. a2b

3(x + y) + 3ab(x + y)

___________________ 3. 7ab2cd

8efg

Write the degree of each polynomial in the blank.

______ 4. 3a – 4 a2 – 3a

3

______ 5. x2y

3 + 3xy

______ 6. 7ab2cd

8efg

9-13. Multiply the polynomials in each problem.

________________________ 9. 4x7(3x

2 – x – 7)

________________________ 10. (7y + 1)(3y – 1)

________________________ 11. (2x2 + 3)( 2x

2 – 3) Recall: these are CONJUGATES & the product will be a difference of perfect squares.

________________________ 12. (7a + 2)(7a + 2) Recall: this will result in a PST – a Perfect Square Trinomial.

___________________________________13. (2a + 3)(a2 – 8a – 3)

___________________________________14. Expand: (x + y)3

Careful! Some students confuse “cubing a binomial” with “factoring the sum of cubes”

___________________________________15. Factor: x3 + y

3

___________________________________16. Expand: (2a + 3)4

Algebra 2 w/ Trig

Semester Exam

Review 9 Polynomials

SOLUTION KEY

Date :

Hint: the DEGREE of any one term is the sum of the exponents on the variables

The DEGREE of an entire polynomial is the highest degree found in any of the terms.

Hint: terms are separated only by + or – signs. A product or quotient is a single term.

Hints: may always use DISTRIBUTIVE PROPERTY repeatedly. (FOIL is a special case of Dist. Prop.)

Hint: use Binomial Theorem and Pascal’s Triangle if you are raising a binomial to a power.