Wednesday

March 4, 2015

March 4, 2015

Posted by **Anonymous** on Monday, August 17, 2009 at 2:04am.

- Algebra -
**MathMate**, Monday, August 17, 2009 at 8:21amIf the question is concerned with a particular term of a polynomial, a coefficient is the numeric or constant (or a combination) part of the term that precedes the variable(s). The exponents are the powers to which the variables are raised.

For example, the first term of the polynomial

5x² + 3x + 1

is 5x².

5 is the coefficient, 2 is the exponent of the variable x.

Thus the operations that we can associate with coefficients are mostly addition and subtraction in the grouping of like terms, such as in simplifying

5x² + 3x + 1 + 4x² + 2x + 3

=(5+4)x² + (3+2)x + (1+3)

= 9² + 5x + 4

Since like terms have variables raised to the same power (exponent), no operations are done on the exponents when grouping like terms.

On the other hand, during a multiplication or division of a polynomial by a monomial (single term) or polynomial, both the coefficients and the variables are multiplied together. For example,

5x² * 4x³

will be calculated as

5x² * 4x³

= (5*4)* x²*x³

= 20 x²*sup3;

= 20 x^{2+3}

= 20x^{5}

Here the coefficients are multiplied together and the exponents are added because of the laws of exponents.

In the less common cases where a term is raised to a power, the coefficient is raised to the same power, while the exponent of the variables are simply multiplied according to the laws of exponents.

For example,

(5x²)²

=(5²)*(x²)²

= 25 * (x^{2*2}

= 25 x^{4}

In short, while both the coefficients and the exponents are subject to the four operations of add, subtract, multiply and divide, the coefficient could be raised to a power in certain cases.

**Answer this Question**

**Related Questions**

Alzebra - What operations can you associate with coefficients? What operations ...

algebra - operations can you associate with coefficients

algebra - what operations can you assocate with coefficients? what operations ...

education - What can you major if you have associate degree in science. What is ...

phi 208 ethical and moral reasoning - Robinson suggests that the more closely ...

i need help completing this MATH question! - ORDER OF OPERATIONS step 1. first ...

algebra - You need to hire a part-time associate to work 30 hours a week in your...

algebra - Question: 89 of 111 Leave Questionnaire You need to hire a part-time ...

algebra - How is doing operations (adding, subtracting, multiplying, and ...

Algebra - How is doing operations (adding, subtracting, multiplying, and ...