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:

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Presentation transcript:

4.3 Polynomials

Monomial: 1 term (ax n with n is a nonnegative 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 Identify monomial, binomial, trinomial, or none None (polynomial) 4x 3 + 4x 2 - 2x - 3 trinomial -2x 2 - 2x +1 binomial 4 + (1/2)x monomial 3x 2 binomial -2x + 4 monomialx4x4

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 has 0 as its coefficient 0

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

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

Arrange in descending order using power of x 1)-6x 2 – 8x 6 + x 8 + 3x - 4 = x 8 – 8x 6 - 6x 2 + 3x - 4 Missing terms are: x 7, x 5, x 4, x 3 2)5y 2 + 4y + 2y = 2y 4 + 5y 2 + 4y + 9 Missing terms are: y 3

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

1) -6x 4 – 8x 3 + 3x x 4 + x 3 + 2x 2 -7x = -6x 4 + 5x 4 – 8x 3 + x 3 + 2x 2 + 3x -7x -4 = -x 4 - 7x 3 + 2x 2 - 4x -4 2)-6x 4 – 8x 3 + 3x x 4 - x 3 - 2x 2 +7x = -6x 4 - 5x 4 – 8x 3 - x 3 - 2x 2 + 3x +7x - 4 = -11x 4 - 9x 3 - 2x 2 +10x -4