Question

How do you factor \[4x + 7\]?

Answer 1

Hint: As we know that the basic equation of finding factors is form of quadratic equation i.e., \[a{x^2} + bx + c = 0\], or expanding the terms given, but here in the given expression consists of only one term, as we want two numbers that multiply together to make ac, and add up to b, hence it does not share any common element.

Complete step-by-step answer:
When factoring a polynomial, the goal is that the GCF of all the terms is one factor. To factor a monomial means to express it as a product of two or more monomials.
In the given expression, none of the terms share a common element that can be taken out, as assume, \[2x - 2\] does, hence we can’t factor the given expression. As this polynomial is not factorable with real numbers.

Note: The key point to find the factors is that when factoring any polynomial is to factor out the GCF. The GCF is the greatest common factor for all the terms of the polynomial. By factoring out the GCF first, the coefficients and constant term of the polynomial will be reduced.
To factor a monomial from a polynomial, we use the following steps:
Write each term as a product of its prime factors.
Determine the greatest common factor (GCF) by underlining the common factors of each term in the polynomial.
Then use the distributive property to factor out the GCF.