How to Factorize a Polynomial of Degree Two?

Mathematics is the easiest subject to learn with practice. Different mathematicians in the history came and designed different techniques to solve polynomials. The general form of the equation of degree "2" is, "ax^2+bx+c=0" with the condition that "a" cannot be equal to zero. This equation is also called quadratic equation because of its degree, which is equal to "2". In this article, we will discuss three methods to solve the polynomials of degree "2". These methods include completing square method, factorization and quadratic formula. The easiest of the three methods is using quadratic formula.

The first method of solving polynomials of degree "2" is "completing square method". Before proceeding towards the solution, you should make sure that the leading coefficient of the equation is "1". If it is not "1", then you should divide each term of the equation with the leading coefficient.

After making the leading coefficient "2", take the constant term in the equation to the right side of equality. Divide the coefficient of the midterm by two, square the answer and add it on both sides. The left side of the equation becomes a complete square. Solve the right hand side and make it a complete square. After that take positive root on both sides and solve two single order linear equations. The solutions of these equations are the factors of the polynomial.

The second popular method of solving polynomial of degree "2" is factorization. In this method, multiple the leading coefficient with the constant coefficient and make all their possible factors. Choose that factors that results in the breaking of the midterm. Use those factors, take the common terms and you will end up with two linear equations. Solve them and get the factors.

The last and the easiest method of solving polynomial equations is quadratic formula. The formula is "x=(-b±√(b^2 - 4*a*c))/2a". Compare the coefficients of the general equations with the given equations, and put them in the quadratic formula. Solve the formula to get the factors of the desired polynomial. The results of all these methods should be the same. If they are not same, then you have committed any mistake while solving the equations.

All these methods are quite popular ones for the easy understanding of the polynomial equations. There are other methods too that can help students to get the factors of the polynomial like "remainder theorem" and "synthetic division". But, these three methods are the basic methods and do not take much time to understand them.

This article is written by an experienced teacher, who is teaching in the field of mathematics and algebra for more than eight years.

Article Source: Muhammad Waqas Ahmed

1 comment:

  1. The degree of a polynomial is the highest degree of its terms, when the polynomial is expressed in canonical form . The degree of a term is the sum of the exponents of the variables that appear in it. The word degree is now standard, but in some older books, the word order may be used instead.