Question

Check whether $3x +7$ is a factor of $3x^2 + 7$.

Answer 1

Hint: Factor is a number or algebraic expression that divides another number or expression evenly leaving no remainder.
Similarly, in the question above we are given an algebraic expression for which we have to find the factors which will leave no remainder for the expression.

Complete step-by-step solution:
Let us learn more about factors first and then we will do the calculation for the expression given.
When two whole numbers or expressions are multiplied, the product of the two numbers will be exactly multiplied by the two numbers leaving no remainder behind. Number 1 is the smallest factor of any number, number 1 and the number itself, number which is divided by the number itself and number 1 then it is called as prime number.
Now we will explain the calculation part of the problem.
$ \Rightarrow 3{x^2} + 7x$ (if we take out the common term from the given expression then we will be able to make the factor of the given expression)
So, from the above expression we will bring out x common;
$ \Rightarrow x(3x + 7)$
Thus, we see that $(3x +7)$ algebraic expression when multiplied with x, it gives $3{x^2} + 7x$ the expression itself.

Therefore, we can say that $3x + 7$ is a factor of the given expression because when it will divide the given expression no remainder will be left behind.

Note: We have some more facts regarding factors such as; when the factors come out to be prime numbers then the factorization is called as prime factorization. Factors are always the whole numbers or algebraic expressions and not the fraction or decimal value. All the even numbers have 2 as their factor.