Fill in the gaps to factorise this expression: [tex]2 x-8=2(--\quad)[/tex]
Answer (1)
Divide each term of the expression by the common factor: 2 2 x = x and 2 − 8 = − 4 .
Place the results inside the parentheses: 2 ( x − 4 ) .
The factored expression is 2 ( x − 4 ) .
Therefore, 2 x − 8 = 2 ( x − 4 ) .
2 ( x − 4 )
Explanation
Understanding the Problem We are given the expression 2 x − 8 and asked to factor it by taking out a factor of 2. This means we want to rewrite the expression in the form 2 × ( something ) .
Finding the Missing Terms To figure out what goes inside the parentheses, we need to divide each term in the original expression by 2. So, we divide 2 x by 2 and − 8 by 2.
Performing the Division Let's do the division:
2 2 x = x
2 − 8 = − 4
Writing the Factored Expression Now we can write the factored expression as 2 ( x − 4 ) . This means the missing terms are x and − 4 .
Final Answer Therefore, the complete factorization is:
2 x − 8 = 2 ( x − 4 )
Examples
Factoring is a technique used to simplify expressions and solve equations. For example, if you are designing a rectangular garden with an area represented by 2 x − 8 square meters, you might want to express the dimensions of the garden in a simpler form. By factoring 2 x − 8 into 2 ( x − 4 ) , you can see that one side of the garden could be 2 meters wide, and the other side would be ( x − 4 ) meters long. This makes it easier to plan the layout and calculate the amount of fencing needed.
