Question

Find the greatest common factor of the terms in the following expression: 10x + 12xyx2 xy2 x2

Answer 1

Step-by-step explanation:

Given:

`10x\text{ + 12xy}`

To find:

the greatest common factor

To determine the greatest common factor, we will factor out the terms and numbers common to both expression

`\begin{gathered} 2\text{ is common to }10x\text{ + 12xy} \\ 10x\text{ = 2\lparen5x\rparen} \\ 12xy\text{ = 2\lparen6xy\rparen} \\ \\ 10x\text{ + 12y = 2\lparen5x\rparen+ 2\lparen6xy\rparen} \\ 10x\text{ + 12y = 2\lparen5x + 6xy\rparen} \end{gathered}`
`\begin{gathered} x\text{ is common to 5x and 6xy} \\ 5x\text{ + 6xy = x\lparen5 + 6y\rparen} \\ 10x\text{ + 12y = 2\lparen x\lparen5 + 6y\rparen} \\ \\ 10x\text{ + 2y = 2x\lparen5 + 6y\rparen} \\ No\text{ number is common to them except 1} \end{gathered}`

Hence, the greatest common factor is 2x