A 30­second commercial aired during the 2007 Super Bowl cost $2,600,000. A 30­second commercial aired during the 1967 Super Bowl cost $40,000. 1) Express these values in scientific notation and 2) Calculate how many times more expensive was it to air a commercial in 2007 than in 1967.
Homework: 7­4 Skills Practice
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Chapter 7­4 Polynomials
Definition: A polynomial is a monomial or the sum of monomials.
A binomial is the sum of two monomials and a trinomial is the sum of three monomials.
Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial:
4y ­ 5xz
6x ­ 4
x2 + 2xy ­7
26b2
4a2b3c­2d4
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­3y ­2y +4y ­1
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Degree of a monomial is the sum of the exponents of all its variables. A constant has a degree of zero.
Degree of a polynomial is the greatest degree of any term in the polynomial.
Examples: 2
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2 3
3a b + 2a ­ x y 5 2
3x + 4x ­7x
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7xy z
8x2 + 7x­2y + 3z
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Standard Form of a Polynomial:
Terms are written with the terms in order from the greatest degree to least degree. When a polynomial is written in standard form, the coefficient of the first term is called the leading coefficient.
Example: 3x2 + 4x5 ­7x in standard form is:
4x5 + 3x2 ­7x and the leading coefficient is 4
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
Yes, trinomial
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
Yes, monomial
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
Yes, binomial
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
No, cannot have a variable in the denominator. This would be a negative exponent!
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
No, negative exponent.
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Find the degree of each polynomial.
0 this is the same as 3x0
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Find the degree of each polynomial.
3: q2 is 2 plus t1 is 1 = 3
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Find the degree of each polynomial.
4
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Find the degree of each polynomial.
6
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Write each polynomial in standard form. Identify the leading coefficient.
leading coef: 2
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Write each polynomial in standard form. Identify the leading coefficient.
leading coef: ­1
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
No. negative exponent.
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial.
Yes. Binomial.
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Find the degree of the polynomial.
5
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Find the degree of the polynomial.
7
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Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial or trinomial. And state the degree of the polynomial.
polynomial; 5
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