POLYNOMIALS

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POLYNOMIALS

• LESSON OBJECTIVES
• Determine the highest degree of a polynomial.
• Writing polynomials in standard form.

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Review

• Lets review some vocabulary. . . . . . .

• Coefficient The number in front of the
  variable.
• Constant A number without a variable.
• Terms Any number, variable, or product or
  quotient of a number and variable. (always
  separated by or signs)

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Polynomial

• These are examples of polynomials

5X² - 2X 3 3X³ 7X - 4
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Degree of a Polynomial
The degree of a polynomial is calculated by
finding the largest exponent in the polynomial.
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Degree of a Polynomial




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Degree of a Polynomial
Largest exponent is 1



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Degree of a Polynomial
Largest exponent is 1 degree 1



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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2


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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2 degree 2


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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2 degree 2
Largest exponent is 3

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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2 degree 2
Largest exponent is 3 degree 3

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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2 degree 2
Largest exponent is 3 degree 3
Largest exponent is n
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Degree of a Polynomial
Largest exponent is 1 degree 1
Largest exponent is 2 degree 2
Largest exponent is 3 degree 3
Largest exponent is n degree n
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Example 1

• Answer the following questions about this
  polynomial

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1. What is the degree of the polynomial?
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Example 1

• Answer the following questions about this
  polynomial

6

1. What is the degree of the polynomial?
2. What is the constant?

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Example 1

• Answer the following questions about this
  polynomial

6

• What is the degree of the polynomial?
• What is the constant?

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Example 1

• Answer the following questions about this
  polynomial

6

1. What is the degree of the polynomial?
2. What is the constant?
3. What is coefficient of third degree term?

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2
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Example 2

• Answer the following questions about this
  polynomial

4

1. What is the degree of the polynomial?
2. What is the constant?
3. What is coefficient of second degree term?

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Standard Form of Polynomials

• When you write polynomials, you write them with
  the exponents in decreasing order.

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Example 3

• Write this polynomial in standard form.

What term has the largest exponent?
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Example 3

• Write this polynomial in standard form.

What term has the next largest exponent?
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Example 3

• Write this polynomial in standard form.

What term has the next largest exponent?
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Example 3

• Write this polynomial in standard form.

What term has the next largest exponent?
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Example 3

• Write this polynomial in standard form.

What term has the next largest exponent?
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Example 3

• Write this polynomial in standard form.

What is the last term?
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TRY THESE Copy them onto notebook paper first,
then re-write in standard form.

• SOLUTIONS
• -3X2 4X
• 4X 9 (stay same)
• -7x2 3x 6
• -11z3 9z2 5z 5
• 15y8 7y5 y
• c2 4c - 2

1. 4x 3x2
2. 4x 9
3. 6 3x 7x2
4. 9z2 11z3 5z 5
5. y 7y5 15y8
6. c2 2 4c

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continued. . .

• SOLUTIONS
• 4q4 3q2 8q 10
• 7x 2
• -x4 2x3 3
• 3x4 2x3 7x 2
• -2x 5
• 3x6 2x2 4
• x3 4x2 2x 5

1. -10 4q4 8q 3q2
2. -2 7x
3. 2x3 x4 3
4. 3x4 2 2x3 7x
5. 5 2x
6. 3x6 4 2x2
7. -2x 5 4x2 x3

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INDEPENDENT PRACTICE (classwork or homework
follow teacher instructions) Copy and re-write
in standard form.

1. 7z3 12 4z
2. 3 3x 4x2 6x3
3. 1 5x 2x2
4. 5y 18y8 3y2
5. -x 4 3x2 - 6x3
6. 9y 9y3 9y2

1. 6x2 7 9x4
2. 3y 9 y3
3. 9 7v
4. 2x 7x2
5. 4x2 2x x3 4
6. -2x 3 5x2