Answer
The constant term is to be analyzed first and next the coefficients of the polynomials when presented with a factoring problem.
Work Step by Step
The quadratic polynomial can be factorized using the steps as follows:
a) The middle term (a term with the power 1) is to be rewritten as the sum of two terms whose product is the same as the product of the term with the highest power and constant term.
b) The four terms so obtained are paired and common are taken so as to obtain the factors.
For instance,
$6x^2 + 8x + 2$
$=6x^2+6x+2x+2$ [$8x$ is to be split, so, the product of term is $(6x^2)(2)=12x^2$]
$=6x(x+1)+2(x+1)$
$=(x+1)(6x+2)$.
$\bf{Special \,\,Remarks}$:
1) If the constant term is zero, then, the variable raised to the lowest power can be taken common and further, factored.
For instance, $y^4 + 11y^3 + 30y^2=y^2(y^2+11y+30)$.
2) There are some polynomials which can be reduced to quadratic polynomials and factored.
For instance, $x^6 - 2x^3 + 1=t^2-2t+1$, where $t=x^2$.
3) The identities of binomial products can be used for factorization as well.
