Because the x^2x2 coefficient is 11 we know the coefficient for the xx terms in the factor will also be 11:
(x )(x )(x)(x)
Because the constant is a negative and the coefficient for the xx term is a negative we know the sign for the constants in the factors will have one positive and one negative because a negative plus a positive can be a negative and negative times a positive is a negative:
(x - )(x + )(x−)(x+)
Now we need to determine the factors which multiply to 48 and when subtracted are -2:
1 xx -48 = -481×−48=−48; 1 - 48 = -47 1−48=−47 <- this is not the factor
2 xx -24 = -482×−24=−48; 2 - 24 = -22 2−24=−22 <- this is not the factor
3 xx -16 = -483×−16=−48; 3 - 16 = -13 3−16=−13 <- this is not the factor
4 xx -12 = -484×−12=−48; 4 - 12 = -8 4−12=−8 <- this is not the factor
6 xx -8 = -486×−8=−48; 6 - 8 = -2 6−8=−2 <- this IS the factor
(x - 8)(x + 6)(x−8)(x+6)
