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Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: We can easily solve problems on factorisation of expressions like this applying simple concepts of greatest common factors and algebraic mathematics. We start solving the given problem by finding the greatest common factor of the first and second term which are $14$ and $7x$ respectively. Upon doing that we can take the greatest common factor out of the bracket as a common of the whole term which gives us the factors of the expression.

Complete step by step answer:
The expression we have is
To find the factors of the above expression we must use the concept of greatest common factors of the two terms in the given expression.
The first term we have is $14$ .
We know that $14$ has the factors $1,\text{ }2,\text{ }7,\text{ }14$ .
Also, the second term in the given expression we have is $7x$ .
We know that $7x$ has the factors $1,\text{ }7,\text{ }x\text{, }7x$ .
We can easily determine that from the two series of factors of $14$ and $7x$ the greatest common factor we have is $7$ .
In the given expression we can rewrite the first and second term individually as an expression of the greatest common factor $7$ as shown below
$=2\cdot 7-7.x$
Now, we take the common factor $7$ as a common from both the terms as shown below
$=7\cdot \left( 2-x \right)$

Therefore, the given expression $14-7x$ has the factors $7$ and $\left( 2-x \right)$.

Note: We must keep in mind that we can only take the common factors from all the terms of the equation out of the bracket. Otherwise, the solution will have errors. Also, to get the correct value of the factors we must be careful while determining the greatest common factor. Any inaccuracy in the solution will lead to incorrect results.
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