Foundations of Algebra 2 Name:
Unit 5 – Day 1 – Evaluating and Terminology of Polynomial Functions Period: Date:
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading
coefficient.
Polynomial # of terms Standard Form? Degree Leading
Coefficient
2( ) 8f x x
4( ) 6 8 3f x x x
4( ) 6g x x
35( ) 10 3
2h x x x
3 2( ) 10 5 1h x x x
Use direct substitution to evaluate the polynomial function for the given value of x.
6. 4 2 3( ) 8 5 3 ; 2f x x x x x x 7.
3 5( ) 4 2 ; 3g x x x x
8. 3( ) 6 25 20; 5h x x x x 9.
4 31 3( ) 10; 4
2 4g x x x x x
Use synthetic substitution to evaluate the polynomial function for the given value of x.
10. 4 3 2( ) 8 12 6 5 9; 2f x x x x x x 11.
3 2( ) 8 7 35; 6g x x x x x
12. 3( ) 8 14 35; 4h x x x x 13.
4 3( ) 2 3 8 13; 2f x x x x x
14. 5 3( ) 6 10 27; 3g x x x x 15.
3 2( ) 7 11 4 ; 3h x x x x x
16. 4( ) 3 20; 4f x x x x
Describe and correct the error n evaluating the polynomial function 4 2( ) 4 9 21 7f x x x x when 2x .
17.
Foundations of Algebra 2 Name:
Unit 5 – Day 2 – Add, Subtract and Multiply Polynomials Period: Date:
Find the sum or difference
1. 2 2( 3 5) ( 4 8 9)x x x x 2. 2 2( 5 7) (5 11 8)z z z z
3. 2 3 2(2 8) ( 4 12 4)a a a a 4. 3 2 2(4 11 4 ) ( 7 5 8)t t t t t
5. 2 4 4 3(3 6 5 6 ) (5 6 4 )y y y y y y 6. 4 2 3 2(8 2 4) (3 12 8 )v v v v v v
7. 2 4 4 3(7 8 11 12 ) (8 11 13 )t t t y y y 8. 4 5 3 2(9 2 11 7) (8 2 8 )m m m m m m
9.
10.
Let 𝑓(𝑥) = 3(𝑥 − 5)2 and 𝑔(𝑥) = −2(𝑥 + 6)2. Which of the following is equivalent to
𝑓(𝑥) + 𝑔(𝑥)?
A. 4𝑥2 + 4𝑥 + 1 C. 𝑥2 − 147
B. 𝑥2 − 54𝑥 + 3 D. 2𝑥 − 54
11.
Which expression must be subtracted from (4𝑥3 − 5𝑥2 + 6𝑥 − 3) to result in
(6𝑥3 − 2𝑥2 + 4𝑥 + 7) ?
A. −2𝑥3 − 3𝑥2 + 2𝑥 − 10 C. −2𝑥3 − 7𝑥2 + 10𝑥 + 4
B. 2𝑥3 + 3𝑥2 − 2𝑥 + 10 D. 2𝑥3 − 7𝑥2 + 10𝑥 + 4
Foundations of Algebra 2 Name:
Unit 5 – Day 3 – Multiply Polynomials using Special Product Patterns Period: Date:
Describe and correct the error in simplifying the expression.
1.
Find the product of the expressions.
2. ( 5)( 5)x x 3. 2( 3 5)( 5)x x x 4.
2( 9)w
5. 2 2( 3 5)( 3 1)x x x x 6.
2( 4)y 7. 4 2 3( 7 )( 5)y y y y
8. 2(2 5)c 9.
2(3 4)t 10. (5 3)(5 3)p p
11. 3(7 )x y 12. (2 9 )(2 9 )a b a b 13.
3(3 7 )x y
14. ( 6)( 6) 8x x x
15. Find the product: (𝑥 − 1)(𝑥 + 5)(𝑥 − 3)
A. 𝑥3 + 15 C. 𝑥3 − 3𝑥2 − 13𝑥 − 15
B. 𝑥3 + 𝑥2 − 17𝑥 + 15 D. 𝑥3 + 7𝑥2 − 7𝑥 + 15
Foundations of Algebra 2 Name:
Unit 5 – Day 4 – Factoring Perfect Squares and Cubes Period: Date:
Factor the polynomials completely.
1. 2 1x 2. 2 100x 3. 24 100x
4. 27 28x 5. 22 144x 6. 5 33 48y y
7. 3 64y 8. 3 216x 9. 33 3x
10. 35 320z 11. 532 2z z
Factor the polynomials completely.
12. 4 25x
13. 4 23 12x x
14. 7 42 16x x
15. 5 410w w
Foundations of Algebra 2 Name:
Unit 5 – Day 5 – Polynomial Synthetic Division Period: Date:
Use Polynomial Synthetic Division to divide the following
1. 2(2 7 10) ( 5)x x x 2.
2(4 13 5) ( 2)x x x
3. 2( 8 1) ( 4)x x x 4.
2( 9) ( 3)x x
5. 3 2( 5 2) ( 4)x x x 6.
3( 4 6) ( 3)x x x
7. 4 3 2( 5 8 13 12) ( 6)x x x x x 8.
4 3( 4 16 35) ( 5)x x x x
Describe and correct the error in these problems
9.
Mixed Review: Factor and solve using X-Box / Shortcut
Solve the equations
11. 2 3 40 0x x 12.
25 13 6 0x x
13. 2 7 2 0x x 14.
24 15 10 0x x
Foundations of Algebra 2 Name:
Unit 5 – Day 6 – Factoring given a factor Period: Date:
Given polynomial f(x) and a factor of f(x), factor f(x) completely.
1. 3 2( ) 10 19 30; 6f x x x x x 2.
3 2( ) 2 40 64; 8f x x x x x
3. 3 2( ) 18 95 150; 10f x x x x x 4.
3 2( ) 9 8 60; 2f x x x x x
5. 3 2( ) 3 2 61 20; 5f x x x x x 6.
3 2( ) 2 15 34 21; 1f x x x x x
7. 3 2( ) 4 25 154 40; 10f x x x x x 8.
3 2( ) 3 4 28 16; 2f x x x x x
Foundations of Algebra 2 Name:
Unit 5 – Day 7 – Solving Given a Factor Period: Date:
If given polynomial f(x) and a factor of f(x), factor f(x) completely. If given polynomial function f(x) and a zero of f(x) find the
other zeros.
1. 3 2( ) 2 21 18f x x x x ; -3
2. 3 2( ) 8 42f x x x x ; ( 7)x
3. 3 2( ) 10 81 71 42f x x x x ;7
4. 3 2( ) 3 28 69 20f x x x x ; 5 5.
3 2( ) 2 5 196 99f x x x x 1
;2
6. 3 2( ) 11 34 104f x x x x ; 13 7.
3 2( ) 14 103 111 18f x x x x ; 6
8. 3 2( ) 2 10 71 9f x x x x ;9 9.
3 2( ) 2 5 32 80f x x x x ; 2 5x
Foundations of Algebra 2 Name:
Unit 5 – Day 8 Listing Possible Zeros for Polynomial Equations Period: Date:
Find all of the possible roots of the following polynomials.
1. 4 3 2( ) 6 7 6 8f x x x x x 2.
3 2( ) 5 4 20f x x x x
Factors of the constant term: Factors of the constant term:
Factors of the leading coefficient: Factors of the leading coefficient:
Possible rational zeros: Possible rational zeros:
Simplified list of zeros: Simplified list of zeros:
3. 4 2( ) 9 4 12f x x x x 4.
3 2( ) 7 15 9f x x x x
Factors of the constant term: Factors of the constant term:
Factors of the leading coefficient: Factors of the leading coefficient:
Possible rational zeros: Possible rational zeros:
Simplified list of zeros: Simplified list of zeros:
5. 3 2( ) 2 2 3f x x x x 6.
4 3 2( ) 4 4 64 192f x x x x x
7. 3 2( ) 2 7 17 10f x x x x 8.
3 2( ) 2 3 8 12f x x x x
9. 3 2( ) 6 11 3 2f x x x x 10.
4 3 2( ) 2 13 19 10 24f x x x x x
11. 4 3 2( ) 8 2 8 78 20f x x x x x 12.
4 3 2( ) 36 24 41 6 8f x x x x x
Foundations of Algebra 2 Name:
Unit 5 – Day 9 – Factoring Polynomials Equations Period: Date:
Find all of the possible roots of the following polynomials.
1. 3 2( ) 2 21 18f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
2. 4 2( ) 13 36f x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
Find all of the possible roots of the following polynomials.
3. 3 2( ) 11 34 104f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
4. 4 2( ) 9 4 12f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
Foundations of Algebra 2 Name:
Unit 5 – Day 10 – Apply the Rational Zero Theorem Period: Date:
Find all of the possible roots of the following polynomials.
1. 3 2( ) 3 19 4 12f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
2. 3 2( ) 2 5 12 14f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
Find all of the possible roots of the following polynomials.
3. 3 2( ) 2f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
4. 3 2( ) 3 2 61 20f x x x x
Factors of the constant term:
Factors of the leading coefficient:
Possible rational zeros:
Simplified list of zeros:
Foundations of Algebra 2 Name:
Unit 5 – Day 11 – Find the Real Zeros Period: Date:
Using the Graph, find all the Real Zeros
1. 2. 3.
4. 5. 6.
Using a Calculator, find all the zeros.
7. 3 2( ) 2 21 18f x x x x 8.
4 3 2( ) 2 13 19 10 24f x x x x x
9. 3 2( ) 6 11 3 2f x x x x
Find the number of solutions or zeroes for each equation or function. Then look at the graph on a
calculator decide how many real solutions and imaginary solutions there are.
10. 3 2( ) 2 2 3f x x x x 11.
4 3 2( ) 8 2 8 78 20f x x x x x
Number of Solutions: __________ Number of Solutions: __________
Number of Real Solutions: __________ Number of Real Solutions: __________
Number of Imaginary Solutions: __________ Number of Imaginary Solutions: __________
Find all the zeroes for each function below.
12. 4 3 2( ) 36 24 41 6 8f x x x x x 13.
3 2( ) 7 15 9f x x x x
Number of Solutions: __________ Number of Solutions: __________
Number of Real Solutions: __________ Number of Real Solutions: __________
Number of Imaginary Solutions: __________ Number of Imaginary Solutions: __________