Final answer:
To factor the expression 3x-30, we find the greatest common factor, which is 3, and pull it out to get 3(x-10). This factors the original expression into a product of a monomial and a binomial.
Step-by-step explanation:
To factor the expression 3x-30, we look for the greatest common factor (GCF) that can be divided evenly into each term. In this case, both terms are divisible by 3. We factor out the 3, and the expression becomes 3(x-10). The bracket now contains a binomial which shows that the number 10 was subtracted from x.
It is similar to the rule for multiplying exponents with the same base, where you add the exponents. For example: xp × xq = x(p+q). However, when factoring, we are doing the reverse of multiplication, which in this case involves finding a common factor and distributing it outside of a binomial.
Remember, when cubing exponentials, you cube the digit term and multiply the exponent by 3. This is a different process than factoring but is another example of handling expressions with exponents.