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How to Factor?

TopPolynomials can be broken into small parts called factors, such that the product of the factors results in the same polynomial. We can factorize a linear equation, quadratic equation or even the cubic polynomial. In order to factorize given polynomial, we use different methods. Let us start with the linear equation i.e. the equation of degree 1. Here the common multiple of the given terms is taken out and the result is obtained. Now we will learn how to factor.
Let us assume the equation 5x + 20. Here we have two terms and we observe that number 5 is common in both terms. So we break the terms as follows:
5 * x + 5 * 4,
= 5 * (x + 4),
So here we find that 5 and (x + 4) are factors of the given expression.
In another situation let us assume a polynomial with degree 2
4x2 + 12x + 9
Here we proceed in such a way that the middle term can be split in two parts such that the sum becomes 12x and the product is equal to the product of the first and third term.
So it can be written as follows:
4x2 + 6x + 6x + 9,
= 2x (2x + 3) + 3 (2x + 3),
Now taking common (2x + 3), we get:
(2x + 3) * (2x + 3),
Also identities can be used to express the polynomial in the form of their factors. Let us take the same polynomial once again. Then we observe that the polynomial 4x2 + 12x + 9 can be written as:
= (2x)2 + 2 * 3 * 2 x + 32,
= (2x + 3)2.