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Polynomials in Several Variables

• Evaluating Polynomials

• Like Terms and Degree

• Addition and Subtraction

• Multiplication

4.7

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Example

Evaluate the polynomial 5 + 4x + xy2 + 9x3y2 for x = 2 and y = 3.

Solution

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Sage and Scribe

• Evaluate the polynomial 5 + 4x + xy2 + 9x3y2 for x = 1 and y = 2.

• 4x2y 3xy + 4y for x=2 and y

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Example

The surface area of a right circular cylinder is given by the polynomial 2rh + r2 where h is the height and r is the radius of the base. A barn silo has a height of 50 feet and a radius of 9 feet. Approximate its surface area.

Solution

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Example

Identify the coefficient and the degree of each term and the degree of the polynomial

10x3y2 15xy3z4 + yz + 5y + 3x2 + 9.Term Coefficient Degree Degree of the

Polynomial

10x3y2

15xy3z4

yz

5y

3x2

9

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Sage and Scribe

• Complete the table: • Complete the table:

Term Coefficient Degree Degree of Polynomia

l

Term Coefficient Degree Degree of Polynomial

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Like Terms

Like, or similar terms either have exactly the same variables with exactly the same exponents or are constants.For example, in the polynomial 10x3y2 15xy3z4 + 1 + 5y + 3x3y2 + 9.

10x3y2 and ______are like termsand

9 and _______are like terms.

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Example

Combine like terms to form equivalent expressions.

10x2y + 4xy3 6x2y 2xy3

Solution

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Sage and Scribe

• Add: (6x3 + 4y 6y2) + (7x3 + 5x2 + 8y2)

• Subtract: (5x2y + 2x3y2 + 4x2y3 + 7y)

(5x2y 7x3y2 + x2y2 6y)

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♦Example

• Multiply(a)

(c)

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Sage and Scribe

• Multiply(a)(x + 6y)(2x 3y)

• Multiply(b) (5x 7y)2

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Sage and Scribe

• Multiply(c)(3x3y2 + 7t)(3x3y2 + 7t)

• Multiply(d) (3x + 1 4y)(3x + 1 +4y)