Question

Correct the error in the expression: 3x^3 +27x=0

a. The factor x^2+9 should have been factored as (x+3)(x+3).
b. The common monomial is not factored out correctly in the first line.
c. The sum of cubes factoring pattern should have been used in the first line.
d. The factor x^2+9 is not a difference of two squares.

Answer 1

The error in the expression 3x^3 + 27x = 0 is that the common monomial x is not factored out correctly. Factoring out x yields x(3x^2 + 27) = 0, which simplifies to x(3)(x^2 + 9) = 0.

Step-by-step explanation:

Correct the error in the expression 3x^3 + 27x = 0. The correct answer is b. The common monomial is not factored out correctly in the first line. To solve this, you would factor out the greatest common factor (GCF) which is x, resulting in x(3x^2 + 27) = 0. Now, we simplify the expression inside the parenthesis, which gives us x(3)(x^2 + 9) = 0. The expression x^2 + 9 cannot be factored as (x + 3)(x + 3) because it's not a difference of two squares and there are no real numbers that satisfy x^2 + 9 = 0. The sum of cubes factoring pattern is also not applicable here since we do not have a sum of cubes.