Question

Two students are in dispute over who factored the expression given below correctly. Daisy factored it to be (2+12)(x-2). Donnie factored it to be 2(+6)(-2). Which one is factored completely and correctly. Explain the reasoning in your work.

Answer 1

Daisy factored it completely and wholly.

Explanation:

An algebraic expression consists of a variable and a number.

Therefore the factors of the algebraic expression must have a variable and a number.

If we look at the factors drawn by both students we find that Donnie's factors do not contain a variable.

For example if we have an expression

x²+ 4x

Then its factors will be x(x+4) . There has to be a variable.

Donnie's factors are missing a variable . There fore these factors do not completely solve the expression.