STAAR EOC Algebra I Factoring — practice questions

1. The definition names the GCF as the largest expression that is a factor of every expression in the list. 2. A shared multiple, rather than a shared factor, is instead what the least common multiple looks for. 3. Adding or multiplying the common factors together does not match the definition, which asks for the single largest one. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_

1. Factor 54 into primes: 54 = 2 times 3 times 3 times 3. 2. Factor 36 into primes: 36 = 2 times 2 times 3 times 3. 3. The factors shared by both numbers are one 2 and two 3s, so multiply 2 times 3 times 3 to get 18. 4. Since the GCF is a factor of both numbers, 54 and 36 can be written as 18 times 3 and 18 times 2. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_

1. Factor the coefficients into primes: 27 = 3 times 3 times 3, and 18 = 2 times 3 times 3. 2. Write the variable parts in expanded form: x cubed is x times x times x, and x to the fourth is x times x times x times x. 3. The common factors are two 3s from the coefficients and three x's from the variables, since x cubed has only three factors of x to share. 4. Multiply the common factors: 3 times 3 times x times x times x gives 9x cubed. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_