warm up. algebra 3 chapter 6 lesson 4 factoring and solving polynomial equations

Warm Up

Multiply the polynomials• 1.

Algebra 3Chapter 6Lesson 4

Factoring and Solving Polynomial Equations

VOCAB

• Factor by grouping – is pairs of terms that have common factors

• Quadratic form – is an expression in the form

CUBESNumber Cubed

1 12 83 274 645 1256 2167 3438 5129 72910 1000

Keep in Mind

• I’m trying to make this as easy as possible…• I’m breaking this lesson into 3 easy parts– It could’ve been 4 but I believe we can do the

zeros part already (we’ve done it in the past)

Warm Up

Factor the polynomial and find the zeros• 1. • 2.

Algebra 3Chapter 6Lesson 4

Factoring and Solving Polynomial Equations

Special Cases

• Sum of Cubes

• Difference of Cubes

Directions (Specials)

• Figure out what a and b are• USE the awesome formula• Reduce• Set equal to zero (to find zeros)• Solve

I DO (Specials)

Factor and Find the zeros• 1. • 2. • 3. • 4.

WE DO (Specials)

Factor and Find the zeros• 1. • 2. • 3. • 4.

YOU DO (Specials)

Factor and Find the zeros• 1. • 2. • 3. • 4.

Question

• How do you know its going to be a sum or difference of cubes?

Review

• Today you learned how to factor a cube

Homework

• Worksheet– 6.4B (1 – 12)

Warm Up

Factor and find the zeros• 1.

Algebra 3Chapter 6Lesson 4

Factoring and Solving Polynomial Equations

Factor By Grouping

• Look at the first 2 terms– Factor it

• Set equal to zero• Solve

I DO (Grouping)

Factor and find zeros• 1. • 2.• 3.• 4.

WE DO (Grouping)

Factor and find zeros• 1. • 2.• 3.• 4.

YOU DO (Grouping)

Factor and find zeros• 1. • 2.• 3.• 4.

Review

• Today you learned how to factor polynomials by grouping

Homework

• 6.4B (13 – 24)

Warm Up

Factor and find the zeros• 1.

Algebra 3Chapter 6Lesson 4

Factoring and Solving Polynomial Equations

Factor By Grouping

• Look at the first 2 terms– Factor it

• Set equal to zero• Solve

I DO (Grouping)

Factor and find zeros• 1.

WE DO (Grouping)

Factor and find zeros• 1.

YOU DO (Grouping)

Factor and find zeros• 1.

Review

• Today you learned how to factor polynomials by grouping

Homework

• 6.4B (13 – 24)

Warm Up

Factor and Find the Zeros• 1.

Divide without a calculator• 3425 by 15

Algebra 3Chapter 6Lesson 5

The Remainder and Factor Theorems

VOCAB• Polynomial Long Division – is one way to divide

polynomials• Synthetic Division – Same thing as synthetic

substitution except with a big polynomial you take the opposite of the constant term

• Remainder Theorem – if the polynomial, , is divided by x-k then the remainder is

• Factor Theorem – a polynomial, , has a factor x-k if and only if

• Divisor – the bottom number of a fraction or the number you are dividing by

Directions (Long Division)• THIS IS EXACTLY LIKE LONG DIVISION WITHOUT A

CALCULATOR• Write the problem in standard form including the

missing terms• Look at the first term in the divisor– Find how many times that goes into the first term of the

polynomial• Multiply that answer times the WHOLE divisor• Subtract that from the polynomial• Keep going until you can’t do anymore• Remainder is then written over the divisor

I DO (Long Division)Divide the polynomial• 1. by • 2. by • 3. by • 4. by

Warm Up

Divide using long division• 1. by

Algebra 3Chapter 6Lesson 5

The Remainder and Factor Theorems

Directions (Long Division)• THIS IS EXACTLY LIKE LONG DIVISION WITHOUT A

CALCULATOR• Write the problem in standard form including the

missing terms• Look at the first term in the divisor– Find how many times that goes into the first term of the

polynomial• Multiply that answer times the WHOLE divisor• Subtract that from the polynomial• Keep going until you can’t do anymore• Remainder is then written over the divisor

We Do (Long Division)Divide the polynomial• 1. by • 2. by • 3. by • 4. by

You Do (Long Division)Divide the polynomial• 1. by • 2. by • 3. by

Review

• What did you learn to do today?

Homework

• Worksheet– 6.5B (1 – 8)

Warm Up

Divide the polynomials• 1. by

Algebra 3Chapter 6Lesson 5

The Remainder and Factor Theorems

Question

• Does anyone know when you can use synthetic division?– Hint look at vocab

Directions (Synthetic Division)• THIS IS EXACTLY LIKE SYNTHETIC SUBSTITUTION• Write the problem in standard form including the

missing terms• Only Write down the coefficients inside• For the outside– Remember to take the opposite of the number

• ANSWER– YOU start with 1 power less than the original

I DO (Synthetic Division)Divide the polynomial• 1. by • 2. by • 3. by • 4. by

We Do (Synthetic Division)Divide the polynomial• 1. by • 2. by • 3. by • 4. by

You Do (Synthetic Division)Divide the polynomial• 1. by • 2. by • 3. by • 4. by

Review

• Today you learned how to divide polynomials using synthetic substitution

Homework

• Worksheet– 6.5B (9 - 16)

Warm Up

IS it LONG DIVISION OR SYNTHETIC DIVISION• 1. by • 2. by • 3. by • 4. by

Algebra 3Chapter 6Lesson 5

The Remainder and Factor Theorems

Directions (Finding Zero’s)

• Do synthetic Division of the function using the given zero

• Set the answer equal to zero• Solve

I DO (Finding Zero’s)Find the zero’s of the polynomial by using the given zero• 1. ; 2• 2. ; 4• 3. ; 10• 4. ; -2

WE DO (Finding Zero’s)Find the zero’s of the polynomial by using the given zero• 1. ; 4• 2. ; 9• 3. ; -3• 4. ; -14

YOU DO (Finding Zero’s)Find the zero’s of the polynomial by using the given zero• 1. ; 8• 2. ; -5• 3. ; 6• 4. ; 3

Review

• Today what did you learn?

Homework

• Worksheet– 6.5B (17 – 20)