Download Algebra 1 9.1 ‐ Adding and Subtracting Polynomials A. Monomials

Algebra 1
9.1 ‐ Adding and Subtracting Polynomials
A. Monomials ‐ a monomial is an expression that is a real number, a variable, or a product of real numbers and variables with whole number exponents. In other words, a monomial is one term.
‐2x
9x2
29xyz
‐15xy5
• Examples: 4
B. Polynomials ‐ a polynomial is either a monomial, or a sum of monomials.
Definition (Polynomial Function)
• P(x) = anxn + an ‐ 1xn ‐ 1 + . . . + a1x + a0 where n is a nonnegative integer and coefficients, an … a0 are real numbers.
• The highest power on a term of the polynomial determines the degree of the polynomial.
• When the polynomial is written in descending order from highest degree to lowest degree, that polynomial is written in standard form. Apr 27­7:50 AM
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NOTE: typically if the degree is higher than 3, we would say “4th degree polynomial, 5th degree polynomial, or 12th degree polynomial.”
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C. Examples. Write each polynomial is standard form. Then classify it by degree and by number of terms.
1.
15x + 2x3
2. ‐12x2 + 3x5 ‐ 18 3. 17x
Apr 27­7:55 AM
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4. x2 ‐ 5 + 2x
5. 3 + x ‐ 7 ‐ 2x
6. x2 + 3x4 ‐ 2x3 ‐ 9 Apr 27­7:55 AM
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7. x5 ‐ 2x + 9
8. 14 + 3x3 ‐ 2x + 4
9. ‐2395x5
Apr 27­7:55 AM
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D. Recall Definitions
• Like Terms ‐ terms that contain the exact same variable expressions raised to the exact same powers
• Coefficient ‐ the number being multiplied by a variable. This number is “attached” or right in front of the variable. • When adding or subtracting polynomials, combine like terms and simply add the coefficients
Write some examples and non‐examples of like terms:
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E. Add or Subtract the following polynomials
10. (10x2 + 4x) + (2x2 ‐ 3x)
11. (‐5m3 + 2m2) ‐ (‐8m3 + m2)
Apr 27­7:57 AM
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12. (‐3g + 4g ‐ 9) ‐ (12 + 2g ‐ 8g)
13. (7h10 + 14h8 ‐ 2) + (‐8h8 ‐ 3h + 4)
Apr 27­7:58 AM
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14. (6t2 + 3t + 7) + (2t2 ‐ 6t ‐ 4)
15. (2y3 + 4y2 ‐ 6) ‐ (5y3 + 2y ‐ 2)
Apr 27­7:58 AM
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9.1 HW p. 497 #s 1 ­ 33 odd
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