POLYNOMIALS
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Unit Overview
In this unit, you will study polynomials in a more detailed manner than you did in previous units. Polynomials are used extensively in geometry and are useful for representing area, volume, gravity, and consumer problems.
Types of Polynomials
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Try this: Find the degree of 2x + 7. Is it linear or quadratic?
Answer: degree = 1, linear
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Try this: Write the polynomial, –2x5 + 7 +2x + 3x2 – 6x3, in standard form.
Answer: –2x5 – 6x3 + 3x2 + 2x + 7
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General Polynomials (02:14)Stop! Go to Questions #1-13 about this section, then return to continue on to the next section.
Multiplying Polynomials
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Try this: a(7x – 4) + 2(–3a + x)
Answer: 7ax – 4a – 6a + 2x
7ax – 10a + 2x
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Stop! Go to Questions #14-17 about this section, then return to continue on to the next section.
Multiplying Binomials
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Try this: (3x – 2)(–4x + 8)
Answer: –12x2 + 24x + 8x – 16
–12x 2 + 32x – 16
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24a11
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Are polynomials closed under multiplication?
Answer: yes!
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Try this: Using difference of squares, find (x + 6)(x – 6)
Answer: x2 – 36
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Try this: Using squaring a binomial, find (7x + 4)2
Answer: 49x2 + 56x + 16
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FOIL Method: Multiplying Binomials (05:18) Stop! Go to Questions #18-21 to complete this unit.
Polynomial Functions
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Applications
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Stop! Go to Questions #22-34 to complete this unit.
