6.1A: Adding and Subtracting Polynomials

6.1A: Adding and Subtracting Polynomials

By Dale Schenewerk

Mr. Schenewerk

Expectations Today:
While I am not here to give you notes, I expect you to take notes and engage just like you would if I were there!

What is a polynomial?

What is a polynomial?

Is it a polynomial?

Multiple Choice

Is the expression $$3x^4-2x^2+7$$ a polynomial?

• 
  Yes

• No because of a negative exponent

• No because an exponent is not a whole number

• No because it contains a square root expression

Multiple Choice

Is the expression $$\frac{4}{x}+x^2-5$$ a polynomial?

• Yes

• No because an exponent is not a whole number.

• No because a variable is in the denominator.

• No, there is a square root in the expression.

Multiple Choice

Is the expression $$\sqrt[]{x}+6x-1$$ a polynomial?

• Yes

• No, an exponent is not a whole number.

• No, a variable is in the denominator.

• No because the square root of x is part of the expression.

Dropdown

In the polynomial shown to the left, this is the leading term

Select answer

​ ​ ​

Math Response

In the polynomial shown, what is the constant term?

Type answer here

Correct Answer: -6

Deg^°

Rad

Degree of a polynomial

Standard Form of a Polynomial

Multiple Choice

Consider the polynomial $$f\left(x\right)=6x^4-3x^2+8x-5$$

Which of the following statements is TRUE?

• The leading term is $$-3x^2$$

• The constant term is $$6$$

• The degree of the polynomial is 4.

• The polynomial is not in standard form.

Multiple Choice

Which term in the expression $$4x^3+2\sqrt[]{x}-7$$ is the reason this expression is NOT a polynomial?

• $$4x^3$$

• $$2\sqrt[]{x}$$

• $$-7$$

Multiple Choice

Which of the following is FALSE about the polynomial?

$$-x^5+4x^3-2x+9$$

• The leading coefficient is -1

• The degree is 5.

• The constant term is 9.

• The polynomial is not in standard form.

Reorder

Reorder the following so that the polynomial would be in standard form.

• $$3x^5$$

• $$-4x^2$$

• $$+x$$

• $$+7$$

1

2

3

4

• 1
• 2
• 3
• 4

Adding Polynomials

Adding Polynomials

Schenewerk's Method

Math Response

Using any method you choose, add the following polynomials.

(Notice in your notes I am going out of order.)

Type answer here

Correct Answer: 4x^2+5x+4

Deg^°

Rad

Math Response

Using any method, add the following polynomials.

Type answer here

Correct Answer: 2x^2+3x+1

Deg^°

Rad

Subtracting Polynomials

Subtracting Polynomials

Schenewerk's Method

Math Response

Using any method, subtract the polynomials.

Notice this is Example B from the notes.

Type answer here

Correct Answer: x^2-2x+13

Deg^°

Rad

Math Response

Using any method, subtract the polynomials.

This is Example A in your notes.

Type answer here

Correct Answer: 6x^2+3x-19

Deg^°

Rad