In Class 2
Student Name: ____________ Block: __________
Algebra 2, Unit 3, Binomial Expansion and Division of Polynomials
Community High School
WARM UP (3 Points)
Exercise 1: Name the parts of the expression.
1. 14b + 25a (EXAMPLE)
2. 30jk – 12m (TRY IT!)
coefficients
14, 25
coefficients
variables
b, a
variables
factors
14, b, 25, a
factors
product 14b – of 14 x b
terms
product
14b and 25b
terms
Exercise 2: Circle the Monomials:
4xy
3
3√ 𝑥
24z2
15pm2n3
2x1/3
Circle Non Examples of Monomials:
4xy
3
3√ 𝑥
24z2
15pm2n3
2x1/3
13𝑥
𝑦
13𝑥
𝑦
12xy + z4
12xy + z4
Write each polynomial in standard form, then classify it by degree and number of terms.
1. 4𝑥 – 6𝑥 + 5
2. 𝑥 2 – 4𝑥 + 3𝑥 5 + 2𝑥
3. 3𝑥 3 + 𝑥 2 – 4𝑥 + 2𝑥 3
___________________________________________________________________________________________________________________________________
Classwork
1. (𝑥 – 3)5
2. (2𝑥 + 4)4
In Class 2
Student Name: ____________ Block: __________
Algebra 2, Unit 3, Binomial Expansion and Division of Polynomials
Community High School
Polynomial long division is a method for dividing a polynomial by another polynomials of a lower degree.
It is very similar to dividing numbers.
Guided Practice:
6. (2𝑥 3 – 9𝑥 2 + 𝑥 + 3) ÷ (2𝑥 + 1)
Simplify the polynomial by performing the indicated operation.
1. 𝑓𝑔(𝑓 4 + 2𝑓 3 𝑔 – 3𝑓 2 𝑔2 + 𝑓𝑔2 )
2. (𝑦 2 − 7𝑦 + 5)(𝑦 2 – 𝑦 – 3)
3. (−𝑥 2 + 2𝑥 3 + 25) ÷ (𝑥 – 3)
4. (2𝑥 – 5)4
In Class 2
Student Name: ____________ Block: __________
Algebra 2, Unit 3, Binomial Expansion and Division of Polynomials
Community High School
8. (15𝑥 2 + 8𝑥 − 12) ÷ (3𝑥 + 1)
9. (𝑥 + 7)2 – (4𝑥 – 10)
1. Synthetic division is a process that can be used as an alternative to long division. Synthetic division
can be used when the divisor is a _____________ binomial with a leading ________________ of one.
Divide using long and synthetic division. Determine whether the given binomial is a factor of p(x).
1. (2𝑥 + 1) ∶ 𝑝(𝑥) = 10𝑥 3 + 7𝑥 2 − 3𝑥 – 5
2. (𝑥 + 3) ∶ 𝑝(𝑥) = 𝑥 3 − 4𝑥 + 11