Question

How do you factor $4x+18$?
(a) Factor by grouping
(b) Zero putting
(c) Guessing the factors
(d) Taking common from coefficients

Answer 1

Hint: To find the factor of the given equation $4x+18$, we will try to analyze the terms to find out if we can take which term can be taken common from the coefficients. We will start off with checking the coefficients of both terms and then check them if we can take anything from both. Then by taking the common we can get the needed answer and factorization.

Complete step by step solution:
We have our given equation as, $4x+18$ and we are to factorize this equation.
So, to start with,
$4x+18$
We have both coefficients as, 4 and 18.
So, as we can easily see, 2 is the common term from both of them as both coefficients 4 and 18 are divisible by 2.
Then, we can take common 2 from $4x+18$.
Thus we have, $2(2x+9)$.
One has to determine all the terms that were multiplied to obtain the given polynomial. Then try to factor every term that you got in the first step and this continues until you cannot factor further. When you can’t perform any more factoring, it is said that the polynomial is factored completely.
Hence the solution is, (d) Taking common from coefficients.

Note: A polynomial $4x+18$ can be written as a product of two or more polynomials of degree less than or equal to that of it. Each polynomial involved in the product will be a factor of it. Monomials can be factorized in the same way as integers, just by writing the monomial as the product of its constituent prime factors. In the case of monomials, these prime factors can be integers as well as other monomials which cannot be factored further.