Question

Two sets of quadratic expressions are shown below in various forms:

Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25
Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25

Which line contains three equivalent expressions?

Answer 1

Line one is equivalent

Answer 2

1.
`x^2 + 3 x +2= x^2 + 2 x + x + 2= x(x+2)+1(x+2)=(x+1)(x+2)\\\\ x^2 + 3 x + 2=(x+(3)/(2))^2-((3)/(2))^2+2=(x+(3)/(2))^2-2.25+2=(x+(3)/(2))^2-0.25`

2.
`x^2 + 5 x + 6 =x^2+ 3 x + 2 x+6=x(x+3)+2(x+3)= (x + 2)(x + 3)\\\\ x^2 + 5 x + 6 =(x+(5)/(2))^2-((5)/(2))^2+6=(x+(5)/(2))^2-6.25+6=(x+(5)/(2))^2-0.25`

Line 1: x² + 3 x + 2= (x + 1)(x + 2)= (x + 1.5)² − 0.25 contains three equivalent expressions.