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Unit #2 Polynomials
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What are we going to do… Find the degree of a polynomial.
Arrange the terms of a polynomial is ascending or descending order.
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Polynomial A polynomial is a monomial or a sum or difference of monomials. Examples 2x x2 – 16 x2 – x – 56
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Binomial A binomial is the sum or difference of two monomials.
Examples x + 1 3x2 – 4x 5xy2 + 3x2yz
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Trinomial A trinomial is the sum or difference of three monomials.
Examples x2 + 2x + 10 4ab2 – ab + 7 -7cd3 – 4cd2 + cd
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POLYNOMIALS Trinomials Binomials
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Degree of a Monomial The degree of a monomial is the sum of the exponents of all its variables. 8y4 degree 4 3a degree 1 -2xy2z3 degree 6 7 degree 0
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Degree of a Polynomial The degree of a polynomial is the greatest degree of any monomial contained in the polynomial. 5mn2 degree 3 -4x2y2 + 3x degree 4 3a + 7ab – 2a2b + 16 degree 3
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Ascending Order To write a polynomial in ascending order, start with the lowest power and work your way to the highest power. x3 + 2x – x2 16 + 2x – x2 + 14x3 REMEMBER: (LOWEST HIGHEST) The sign in front of the numbers, stays with the number!
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Descending Order To write a polynomial in descending order, start with the highest power and work your way down to the lowest power. a4 + ax2 – 2a3xy3 – 9x4y -9x4y + ax2 – 2a3xy3 + a4 REMEMBER: (HIGHEST LOWEST) The sign in front of the number, stays with the number!
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Find the degree: Example 1:
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Example 2: 2x3 – 4y + 7xy degree 3
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Example 3: 7 + d5 – b2c2d3 + b6 degree 7
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Example 1: Arrange the polynomial in ascending order:
2x + 3x2 – 1 -1 + 2x + 3x2
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Example 2: Arrange the polynomial in ascending order:
-5x2 + 3x + 4x5 - 2 -2 + 3x - 5x2 + 4x5
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Example 3: Arrange the polynomial in ascending order:
-4x2y + 3xy – 5x3y2 3xy – 4x2y – 5x3y2
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Example 4: Arrange the polynomial in descending order:
5 + x5 + 3x3 x5 + 3x3 + 5
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Example 5: Arrange the polynomial in descending order:
-1 + 3x2 + 2x 3x2 + 2x - 1
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Example 6: Arrange the polynomial in descending order:
-3x2y2 + 2xy – 3x3y -3x3y – 3x2y2 + 2xy
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