Question

7-107. Identify the terms, coefficients, constant terms, and factors in each expression below.

a. 3x2 + (−4x) + 1
b. 3(2x − 1) + 2

Answer 1

a. Terms:
`3x^(2), 4x , 1`

Coefficients: 3, -4

Constant terms: 1

Factors: (3x -1) and (x -1)

b. Terms: 6x, -1

Coefficients: 6

Constant terms: -1

Factors: No factors

Explanation:

The given expressions are:

a.
`3x^2 + (-4x) + 1`

b. 3(2x -1) + 2

Let's take the first expression

`3x^2 + (-4x) + 1` can be written as
`3x^2 -4x + 1` because +(-4x) = -4x

Terms:
`3x^(2), 4x , 1`

Coefficients: 3, -4

Constant terms: 1

Factors:

`3x^2 -4x + 1`

=
`3x^2 - 3x -1x + 1\\= 3x(x - 1) -1(x -1)\\= (3x -1)(x-1)`

So, the factors are (3x -1) and (x -1)

Let's take second expression.

3(2x -1) + 2

Let's simplify this. Using the distributive property a(b -c) = ab - ac

3(2x -1) + 2 = 3(2x) +3(-1) + 2

= 6x - 3 + 2

= 6x -1

Terms: 6x, -1

Coefficients: 6

Constant terms: -1

Factors:

No factors

Answer 2

a. The terms are: (1) 3x² , (2) -4x and, (3) 1
coefficients: (1) 3 and (2) - 4
constant term: 1

b. 3(2x - 1) + 2
This can be simplified into: 6x - 3 + 2 = 6x - 1
terms are: 6x and -1
coefficients: 6
constant term: -1