2. Monomial and polynomial
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  1. Definition of term

   The algebraic expression  -3x2  is a term and 2a5  is another term.

  A term is a conjoint constituted by four elements: the sign, the coefficient, the literal part and the exponent.

   -3x2  The sign here is negative, the coefficient is 3, the literal part is x and the  exponent is 2.

   +2a  The sign is positive, the coefficient is 2, the literal part is a but it has no exponent. When a term has no exponent it is supposed that the exponent is 1.

   7n5  It has no sign, so it is supposed that the sign will be positive, the coefficient is 7, the literal part is n and the exponent is 5.

   -n3  It has negative sign, no coefficient and is supposed that its coefficient is 1, its literal part n and the exponent 3.

   x It has no sign and it is supposed that is positive. It has no coefficient, so it is supposed it is 1. Its literal part is x. It has no exponent, so we supposed it will be 1.

   A term without a literal part is called an independent term.

   The algebraic expression  -3x2  is a term and 2a5  is another term.

  A term is a conjoint constituted by four elements: the sign, the coefficient, the literal part and the exponent.

   -3x2  The sign here is negative, the coefficient is 3, the literal part is x and the  exponent is 2.

   +2a  The sign is positive, the coefficient is 2, the literal part is a but it has no exponent. When a term has no exponent it is supposed that the exponent is 1.

   7n5  It has no sign, so it is supposed that the sign will be positive, the coefficient is 7, the literal part is n and the exponent is 5.

   -n3  It has negative sign, no coefficient and is supposed that its coefficient is 1, its literal part n and the exponent 3.

   x It has no sign and it is supposed that is positive. It has no coefficient, so it is supposed it is 1. Its literal part is x. It has no exponent, so we supposed it will be 1.

   A term without a literal part is called an independent term.

  A. Choose the correct answer: a, b, c. 

  1. In the term -7x3 , 7 is

    a.  the literal part
    b.  the sign
    c.  the coefficient

  

  2. In the term  -7x2, 2 is

    a.  the exponent
    b.  the coefficient
    c.  the literal part

  

 3. In the term 4x3, x is

    a.  the coefficient
    b.  the literal part
    c.  the exponent

  

 4. In the term 6m4, the sign is

    a.  positive
    b.  negative
    c.  the exponent

  

 5. In the term  -x3 the coefficient is

    a.  cero
    b.  one
    c.  infinite

  

 6. In the term  +8y2 ,el 8 is the

    a.  exponent
    b.  sign
    c.  coefficient

  

  2. Defining monomial and polynomial

   3x2 + 3x  is a polynomial and 18x2  is a monomial.

   A monomial is a conjoint constituted by a single term.

   a2x  y  a3y are monomial.

  A polynomial is a conjoint constituted by two or more terms.

   a2 + b2is a polynomial constituted by two terms. It is also called binomial. The term a2 has a positive sign.

   -x2  +  2xy  +  y2 is a polynomial constituted by three terms, and is also called trinomial.

   ax  +  by  -ay  -bx  is a polynomial constituted by four terms.  ax has positive sign because it has no a visible sign and is at the beginning of the polynomial.  

  B. Choose the correct answer: a, b, c.

  1. The term 3y4  is a

    a.  monomial
    b.  binomial
    c.  trinomial

  

  2. The sign of the term  3y4  is

    a.  negative
    b.  positive

  

 3. The expression  -x3 + 3x2y  +  y2  is a

    a.  monomial
    b.  binomial
    c.  trinomial

  

 4. The expression  a3 + b2  is a

    a.  monomial
    b.  binomial
    c.  trinomial

  

 5. When an algebraic expression has a single term is called

    a.  monomial
    b.  binomial o polynomial
    c.  trinomial o polynomial

  

 6. If the first term has no sign, it will be

    a.  negative
    b.  positive

  

  3. Order in polynomials

To put order in a polynomial in relation to a letter, we must write the terms. The exponents of the letter must be placed in descending order from first to last.

   Example: Order the polynomial in accordance with x:

   mnx2y - 8mx3 - 2mnxy2 + 6n3y

   Answer: - 8mx3 + mnx2y - 2mnxy2 + 6n3y

  C. Choose the correct answer: a, b or c.

  1. Order the following polynomial according to m : 5m2x2  + 3mx3  + 5m3x  +  x4  + m4

    a.  x4  + m4  5m2x2  + 3mx3  + 5m3x
    b.  x4  +  3mx3  +  5m2x2  + 5m3x  + m4
    c.  m4  +  5m3x  +  5m2x2  +  3mx3  + x4

  

  2. Order the following polynomial according to a: 5a3b  + 3b4  -  3a2b2  - 7ab2

    a.  5a3b  - 3a2b2  - 7ab2  + 3b4
    b.  3b4  -  3a2b2  - 7ab2  +  5a3b 
    c.  -7ab2  -  3a2b2  +  3b4  +  5a3b

  

 3. Order the following polynomial according to x:  mnx2y  -  8mx3  -  2mnxy2  +  6n3y

    a.  - 2mnxy2  +  mnx2y  +  6n3y  -  8mx3
    b.  -8mx3  +  mnx2y  -  2mnxy2  +  6n3y
    c.  mnx2y  +  6n3y -  8mx3  -  2mnxy2

  

 4. Order the following polynomial according to a:  8a2c2  +  3a4  -  5a3c  +  4ac3

    a.  3a4  - 5a3c  +  8a2c2  +  4ac3
    b.  4ac3  +  8a2c2  -  5a3c  +  3a4
    c.  3a4  -  5a3c  +  4ac3 +  8a2c2

  

 5. Order the following polynomial according to a:  25a2c  -  45ac2  -  18a3  + 5c3

    a.  -45ac2  +  25a2c  -  18a3  +  5c3
    b.  -18a3  +  25a2c  -  45ac2  +  5c3
    c.  5c3  -  45ac2  +  25a2c  -  18a3

  

 6. Order the following polynomial according to y:  2ay2 - y3  - 5a2y  +  a3

    a.  a3  -  5a2y  +  2ay2  -  y3
    b.  -5a2y  +  2ay2  -  y3 +  a3
    c.  -y3  +  2ay2  -  5a2y  +  a3

  


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