Final answer:
Josh made an error in factoring the expression by incorrectly writing the factors after taking out the common factor '-4'. The correct factored form of the expression -20 - 8 + 12b is -4(-5 + 2 - 3b), where the numeric terms and coefficients are correctly simplified after factoring out -4.
Step-by-step explanation:
Josh is trying to factor the expression -20 - 8 + 12b. However, he makes an error in the factoring process. The correct way to factor this expression is to find a common factor for all terms. In this case, the common factor is -4, which when factored out should give us the expression -4(-5 + 2 - 3b). This is because -4 multiplied by -5 gives us 20, -4 multiplied by 2 gives us -8, and -4 multiplied by -3b gives us 12b.
So, the error Josh made was in the signage of the factored terms. He also seems to have included an 'a' erroneously instead of simplifying the numeric terms and maintains a mistake in the coefficient of 'b'. Josh likely wrote the number 36 instead of 3 by mistake, likely from misinterpreting the necessary division by -4 to factor out. The correct factored form should be -4(-5 + 2 - 3b).