Chapter R4, Problem 1PE

To determine

The correct word or phrase to fill the blank.

Answer to Problem 1PE

Solution:

  $\left(a\right)$ Given the expression $8x+cd-3y+90$ , the terms $8x,cd\text{and}-3y$ are variable terms, whereas $90$ is a constant term.

  $\left(b\right)$ The constant factor in a term is called the coefficient.

  $\left(c\right)$ Given the expression $x$ , the value of the coefficient is $1$ , and the exponent is $1$.

  $\left(d\right)$ Terms that have the same variables, with corresponding variables raised to the same powers are called liketerms.

Explanation of Solution

Given:

  $\left(a\right)$ Given the expression $8x+cd-3y+90$ , the terms $8x,cd\text{and}-3y$ are variable terms, whereas $90$ is a ______ term.

  $\left(b\right)$ The constant factor in a term is called the ______

  $\left(c\right)$ Given the expression $x$ , the value of the coefficient is ______, and the exponent is ______.

  $\left(d\right)$ Terms that have the same variables, with corresponding variables raised to the same powers are called ______ terms.

Calculation:

To fill the given blanks with appropriate words, we will use below concepts:

A term is a constant or the product of a constant and one or more variables. For example, in the expression $7x^2+2xy+5$ , $7x^2,2xy\&5$ are terms.

The terms $7x^2,2xy$ are variables terms whereas $5$ is a constant.

The constant factor in a term is called coefficient of the term.

Like terms are terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only like terms can be combined.

Basis the above concepts, we can fill the blanks with appropriate word.

  $\left(a\right)$ Given the expression $8x+cd-3y+90$ , the terms $8x,cd\text{and}-3y$ are variable terms, whereas $90$ is a constantterm.

  $\left(b\right)$ The constant factor in a term is called the coefficient

  $\left(c\right)$ Given the expression $x$ , the value of the coefficient is $1$ , and the exponent is $1$.

  $\left(d\right)$ Terms that have the same variables, with corresponding variables raised to the same powers are called liketerms.

Conclusion:

Basis the concepts of terms, factors and the coefficient, we could fill the blanks.