Factor the expression 5x + 7x.

Factor the expression 5x + 7x.

• A. 12x
• B. x(5 + 7)
• C. (5x)(7)
• D. x^2(5 + 7)

Answer: (B)

Pull out the common factor. Both terms have an x, so you factor x out and write the inside as the sum of the remaining coefficients: x times (5 + 7). This shows the expression as a product, which is what factoring accomplishes. If you distribute, you get back 5x + 7x, so nothing is lost—just rewritten in a factored form. The other forms don’t represent factoring: they either leave the expression as a sum of terms, or multiply the factors in a way that changes the expression (for example, introducing an extra x or combining the coefficients in a way that isn’t how the original terms were formed).

Pull out the common factor. Both terms have an x, so you factor x out and write the inside as the sum of the remaining coefficients: x times (5 + 7). This shows the expression as a product, which is what factoring accomplishes. If you distribute, you get back 5x + 7x, so nothing is lost—just rewritten in a factored form.

The other forms don’t represent factoring: they either leave the expression as a sum of terms, or multiply the factors in a way that changes the expression (for example, introducing an extra x or combining the coefficients in a way that isn’t how the original terms were formed).