3.1 Alg 2 Polynomial Long Division

3.1 Alg 2 Polynomial Long Division

What did we do with the remainder in writing the final answer?

What does it mean if there is a remainder?

What does it mean if there is NO REMAINDER?

Now we are going to apply this idea to POLYNOMIAL DIVISION. Here are the steps:

Step 1: Set up the problem. Are polynomials in standard form? is a placeholder needed?

Step 2: Divide, and write something on top

Step 3: Multiply by what is outside

Step 4: Subtract

Repeat until you cannot divide any longer.

Write final answer in proper format (if there is a remainder).

***If there is no remainder, that means the divisor is a factor of the dividend BUT IF THERE IS a remainder, the divisor IS NOT A FACTOR of the dividend.

Multiple Choice

When dividing polynomials, if there IS NO remainder, then

• The divisor is a factor of the polynomial

• The divisor is not a factor of the polynomial

• The polynomials don't work

• Then it is not a polynomial

Multiple Choice

When dividing polynomials, if there IS a remainder, then

• The divisor is a factor of the polynomial

• The divisor is not a factor of the polynomial

• The polynomials don't work

• Then it is not a polynomial

Multiple Choice

The divisor, (x-3) is a factor of the polynomial. 

 $\$  

• True

• False

Multiple Choice

The divisor, 

 $x^2-2x+1$  is a factor of the polynomial. 

• True

• False

Here are the steps for polynomial long division:

Step 1: Set up the problem, Are polynomials in standard form? is a placeholder needed?

Step 2: Divide, and write something on top

Step 3: Multiply by what is outside

Step 4: Subtract

Repeat until you cannot divide any longer.

Write final answer in proper format (if there is a remainder).

***If there is no remainder, that means the divisor is a factor of the dividend BUT IF THERE IS a remainder, the divisor IS NOT A FACTOR of the dividend.

Multiple Choice

What is the first step in polynomial long division?

• Subtract

• Multiply by the outside terms

• Divide and put something on top

Multiple Choice

What is the second step in polynomial long division?

• subtract

• multiply by the outside terms

• divide and put something on top

Multiple Choice

What is the next step in long division?

Put something up top (after you divide), Multiply by the outside terms, and then...

• Bring the next thing down

• Add the terms

• Start Over

• Subtract the terms

Multiple Choice

Is this division problem worked correctly?

• This is correct!
• This is incorrect!

Multiple Choice

Is this problem worked correctly?

• This is correct

• This is incorrect

Here are the steps for polynomial long division:

Step 1: Set up the problem, Are polynomials in standard form? is a placeholder needed?

Step 2: Divide, and write something on top

Step 3: Multiply by what is outside

Step 4: Subtract

Repeat until you cannot divide any longer.

Write final answer in proper format (if there is a remainder).

***If there is no remainder, that means the divisor is a factor of the dividend BUT IF THERE IS a remainder, the divisor IS NOT A FACTOR of the dividend.

Multiple Choice

What should you add when setting up this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

• 0x⁴

• 0x³

• 0x²

• 0x

Here are the steps for polynomial long division:

Step 1: Set up the problem, Are polynomials in standard form? is a placeholder needed?

Step 2: Divide, and write something on top

Step 3: Multiply by what is outside

Step 4: Subtract

Repeat until you cannot divide any longer.

Write final answer in proper format (if there is a remainder).

***If there is no remainder, that means the divisor is a factor of the dividend BUT IF THERE IS a remainder, the divisor IS NOT A FACTOR of the dividend.

BREAKOUT ROOM...

TAKE A PICTURE OF THE NEXT PROBLEM AND WORK ON IT WITH YOUR PARTNER. Be prepared to answer qustions about the problem when I visit or when we come back together.

Time to Practice!

IXL: Lesson L4