Question

Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Completely factor the following expressions.
 
  4x - 12 =

  1/4 x + 3/4=

  0.3 x - 1.5 =
 

Answer 1

1) 4(x- 3)

2)
`(1)/(4)(x+3)`

3) 0.3(x - 0.5)

Explanation:

Given some expressions.

`4x - 12\\\\ (1)/(4)x+(3)/(4)\\\\0.3 x - 1.5`

We have to factor the given expression completely.

Factorization is the process of writing an expression in form of lower factors so that when we multiply them we get back the original expression.

Consider 1 ) 4x - 12

Taking 4 common from each term, we get

⇒ 4x - 12 = 4(x- 3)

Consider 2 )
`(1)/(4)x+(3)/(4)`

Taking
`(1)/(4)` common from each term, we get

⇒
`(1)/(4)x+(3)/(4)=(1)/(4)(x+3)`

Consider 3 ) 0.3x - 1.5

Taking 0.3 common from each term, we get

⇒ 0.3x - 1.5 = 0.3(x - 0.5)

Answer 2

The correct answers are:
4(x-3)
0.25(x+3)
0.3(x-5).

Explanation:
The GCF, greatest common factor, of 4x and 12 is 4.
We factor this out, placing it outside parentheses.
We then divide both 4x and -12 by 4;

`(4x)/(4) = 1x` and
`(-12)/(4)`
`=-3`,
giving us 4(1x-3) or 4(x-3).

The GCF of 0.25x+0.75 is 0.25.
We factor this out, placing it outside parentheses.
We then divide 0.25x and 0.75 by 0.25;

`(0.25x)/(0.25) = 1x` and
`(0.75)/(0.25) = 3`,
giving us 0.25(x+3).

The GCF of 0.3x and 1.5 is 0.3.
We factor this out, placing it outside parentheses.
We then divide 0.3x and -1.5 by 0.3;

`(0.3x)/(0.3) = 1x` and
`(-1.5)/(0.3) = -5`,
giving us 0.3(1x-5).