Matt Wolf



Directions: Find all zeros and write the complete linear factorization of [pic].

Pre-Calculus/Trigonometry3 Name: ____________________________

Zeros of Polynomial Functions II

Worksheet

Directions: Find all zeros and write the complete linear factorization of [pic].

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Identifying All Zeros of a Function

Methods

• Factoring: GCF, Trinomials, DOTS, and Grouping

• Quadratic Formula: Applied to second degree functions that do not factor.

• Rational Root Test: Applied to functions of greater than second degree that do not factor.

• Division: Applied if you are given a zero/factor of [pic]. Use the zero/factor to

break down the function by long division or synthetic division.

• Long Division: Applied for dividing functions by factors of degree greater than one.

• Synthetic Division: Applied for dividing functions by factors of the form[pic].

Types of Zeros

• Rational: If [pic] is a zero of [pic], then [pic] is a factor of [pic]

• Irrational: If [pic] is a zero of [pic], then [pic] is also a zero of [pic]

• Complex: If [pic] is a zero of [pic], then the complex conjugate [pic]

is also a zero of [pic]

Pre-Calculus/Trigonometry3 Name: ____________________________

Zeros of Polynomial Functions II

Worksheet

Pre-Calculus/Trigonometry3 Name: ____________________________

Zeros of Polynomial Functions II

Worksheet

Identifying All Zeros of a Function

Methods

• Factoring: GCF, Trinomials, DOTS, and Grouping

• Quadratic Formula: Applied to second degree functions that do not factor.

• Rational Root Test: Applied to functions of greater than second degree that do not factor.

• Division: Applied if you are given a zero/factor of [pic]. Use the zero/factor to

break down the function by long division or synthetic division.

• Long Division: Applied for dividing functions by factors of degree greater than one.

• Synthetic Division: Applied for dividing functions by factors of the form[pic].

Types of Zeros

• Rational: If [pic] is a zero of [pic], then [pic] is a factor of [pic]

• Irrational: If [pic] is a zero of [pic], then [pic] is also a zero of [pic]

• Complex: If [pic] is a zero of [pic], then the complex conjugate [pic]

is also a zero of [pic]

Pre-Calculus/Trigonometry3 Name: ____________________________

Zeros of Polynomial Functions II

Worksheet

1) [pic] Zeros:[pic]_____________ [pic]___________________________

2) [pic] Zeros:[pic]_____________ [pic]___________________________

3) [pic] Zeros:[pic]_____________ [pic]___________________________

4) [pic] Zeros:[pic]_____________ [pic]___________________________

5) [pic] Zeros:[pic]_____________ [pic]___________________________

6) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

7) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

8) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

9) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

10) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

1) [pic] Zeros:[pic]_____________ [pic]___________________________

2) [pic] Zeros:[pic]_____________ [pic]___________________________

3) [pic] Zeros:[pic]_____________ [pic]___________________________

4) [pic] Zeros:[pic]_____________ [pic]___________________________

5) [pic] Zeros:[pic]_____________ [pic]___________________________

6) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

7) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

8) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

9) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

10) [pic]

given that [pic]is a zero Zeros:[pic]_____________ [pic]___________________________

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