Algebra of Educational applications for mobiles

Un término es un conjunto formado por cuatro elementos: el signo, el coeficiente, la parte literal y el exponente. -3x2 El signo es negativo, coeficiente 3, parte literal x y exponente 2. +2a El signo es positivo, coeficiente 2, parte literal a, pero no tiene exponente.

Cuando un término no tiene exponente se presupone que el exponente es 1. 7n5 No tiene signo y se supone que su signo es positivo, el coeficiente es es 7, la parte literal es n y el exponente 5. -n3 Tiene signo negativo, no tiene coeficiente y se sobreentiende que su coeficiente es 1, la parte literal es n y el exponente es 3. x No tiene signo y se entiende que es positivo. No tiene coeficiente y se sobreentiende que es 1. Su parte literal es x. No tiene exponente y se sobreentiende que es 1. Un término que no tiene parte literal se llama término independiente.

B. 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

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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®Arturo Ramo García.-Record of intellectual property of Teruel (Spain) No 141, of 29-IX-1999 Plaza Playa de Aro, 3, 1º DO 44002-TERUEL