Answer:
The sum of the factors is 13.
Step-by-step explanation:
The factor with a greater absolute value is positive. If |a|>|b|, then the two factors of -48 are a and b, where a is positive and b must be negative.
[tex]a\times b=-48[/tex]
[tex]ab=-48[/tex] ... (1)
The difference of factors is 19.
[tex]a-b=19[/tex]
[tex]a=19+b[/tex] ... (2)
From (1) and (2), we get
[tex](19+b)b=-48[/tex]
[tex]19b+b^2+48=0[/tex]
[tex](b+16)(b+3)=0[/tex]
[tex]b=-16,-3[/tex]
If b=-16, then using equation (1) the value of a is 3. Here |b|>|a|, so this condition is not true.
If b=-3, then using equation (1) the value of a is 16. Here |a|>|b|, so this condition is true. Therefore the two factors of -48 are 16 and -3.
The sum of two factors of -48 is
[tex]16+(-30)=16-3=13[/tex]
Therefore the sum of the factors is 13.
