Question

Factor completely: 3x2 − 17x − 28

Answer 1

The answer is (3x+4)(x-7)

Answer 2

`3x^(2) -17x-28=(x-7)(3x+4)`

Explanation:

we have

`3x^(2) -17x-28`

equate to zero

`3x^(2) -17x-28=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2) -17x=28`

Factor the leading coefficient

`3(x^(2) -(17/3)x)=28`

Complete the square. Remember to balance the equation by adding the same constants to each side

`3(x^(2) -(17/3)x+(289/36))=28+(289/12)`

`3(x^(2) -(17/3)x+(289/36))=(625/12)`

`(x^(2) -(17/3)x+(289/36))=(625/36)`

Rewrite as perfect squares

`(x-(17/6))^(2)=(625/36)`

`(x-(17/6))=(+/-)(25/6)`

`x=(17/6)(+/-)(25/6)`

`x=(17/6)(+)(25/6)=42/6=21/3`

`x=(17/6)(-)(25/6)=-8/6=-4/3`

so

`3x^(2) -17x-28=3(x-(21/3))(x+(4/3))`

`3x^(2) -17x-28=(1/3)(3x-21)(3x+4)`

`3x^(2) -17x-28=(x-7)(3x+4)`