Question

How do you rewrite the expression by factoring out the GCF: \[7 + 49x\] ?

Answer 1

Hint: We have a simple algebraic expression. We know that GCF is the greatest common factor. The greatest common factor is the greatest factor that divides the two numbers. We first find the GCF of the two numbers 7 and 48 and then we take that number as common in both the terms.

Complete step by step solution:
Given,
 \[7 + 49x\]
Now to find the GCF of 7 and 49.
WE know that factors of 7 are only 1 and 7.
We know that the factors of 49 are 1, 7 and 7.
That is
 \[7 = 1 \times 7\]
 \[49 = 1 \times 7 \times 7\] .
We can see that the greatest factor that divides the two numbers is 7.
Hence GCF is 7.
Now take 7 common we have,
 \[ \Rightarrow 7\left( {1 + 7x} \right)\]
Thus \[7 + 49x\] can be expressed by factoring out the GCF is \[7\left( {1 + 7x} \right)\]
So, the correct answer is “ \[7\left( {1 + 7x} \right)\] ”.

Note: Be careful in finding the GCF of the two numbers. T0 check our solution, apply the distributive property \[a(b + c) = ab + ac\] in the answer, to get the expression given in the problem, if it is equal to the expression, the solution is correct otherwise we have made a mistake.