Question

Factor completely: 3x2 − 17x − 28

Answer 1

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

Answer 2

Answer:

$3x^{2} -17x-28=(x-7)(3x+4)$

Step-by-step 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

$3x^{2} -17x-28=3(x-(21/3))(x+(4/3))$

$3x^{2} -17x-28=(1/3)(3x-21)(3x+4)$

$3x^{2} -17x-28=(x-7)(3x+4)$