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4.3 Polynomials

4.3 Polynomials. Monomial: 1 term (ax n with n is a non-negative integers) Ex: 3x, -3, or 4y 2 Binomial: 2 terms Ex: 3x - 5, or 4y 2 + 3y Trinomial: 3 terms Ex: 4x 2 + 2x - 3. Polynomial: is a monomial or sum of monomials Ex: 4x 3 + 4x 2 - 2x - 3 or 5x + 2

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4.3 Polynomials

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  1. 4.3 Polynomials

  2. Monomial: 1 term (axn with n is a non-negative integers) Ex: 3x, -3, or 4y2 • Binomial: 2 terms Ex: 3x - 5, or 4y2 + 3y • Trinomial: 3 terms Ex: 4x2 + 2x - 3

  3. Polynomial: is a monomial or sum of monomials Ex: 4x3 + 4x2 - 2x - 3 or 5x + 2 Identify monomial, binomial, trinomial, or none x4 monomial -2x + 4 binomial monomial 3x2 trinomial -2x2 - 2x +1 None (polynomial) 4x3 + 4x2 - 2x - 3 binomial 4 + (1/2)x

  4. Term: each monomial of the polynomial • Degree: exponents • Degree of polynomial: highest exponent • Coefficient: number in front of variables • Constant term: the term without variable • Missing term: the term that has0 as itscoefficient 0

  5. Ex: -3x4 – 4x2 + x – 1 Term: -3x4 , – 4x2 , x, – 1 Degree 4 2 1 0 Coefficient -3 -4 1 -1 Degree of this polynomial is 4 Constant term: is -1 Missing term (s): is x3

  6. Descending order: exponents decrease from left to right • Ascending order: exponents increase from left to right • When working with polynomials, we often use Descending order

  7. Arrange in descending order using power of x • -6x2 – 8x6 + x8 + 3x - 4 = x8– 8x6 - 6x2 + 3x - 4 Missing terms are: x7, x5, x4, x3 • 5y2 + 4y + 2y4 + 9 = 2y4 +5y2 + 4y + 9 Missing terms are: y3

  8. Collecting Like Terms • Like terms: 4x and 3x 5xy and -6xy 2x2 and x2 When add or subtract like-term, add or subtract only the coefficients of the terms, keep the same variables

  9. 1) -6x4 – 8x3 + 3x - 4 + 5x4 + x3 + 2x2 -7x = -6x4 + 5x4 – 8x3 + x3 + 2x2 + 3x -7x -4 = -x4 - 7x3 + 2x2 - 4x -4 • -6x4 – 8x3 + 3x - 4 - 5x4 - x3 - 2x2 +7x = -6x4 - 5x4 – 8x3 - x3 - 2x2 + 3x +7x - 4 = -11x4 - 9x3 - 2x2 +10x -4

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