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. 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

Answer 2

Answer:

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

Step-by-step 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