Question

How do you factor quadratics by using the grouping method?

Answer 1

Hint: In this question, we have to find the factor of a quadratic equation. So, we will apply the grouping method, to get the solution. As we know, a quadratic equation is a type of equation where we have the highest power equals to 2. Thus, when we factor a quadratic equation, we get two linear polynomials. So, we will first let a general quadratic equation and then, split the middle term as the sum of the two term which is equal to the factors of the product of the coefficient of ${{x}^{2}}$ and the constant. After that, we will take common terms in the first two terms and other common terms in the last two terms, to get the required solution.

Complete step by step solution:
According to the question, we have to find the factors of a quadratic equation
Thus, to solve this problem we will use the grouping method to get the solution.
Let us suppose the general form of the quadratic equation is $a{{x}^{2}}+bx+c=0$, where a is the coefficient of ${{x}^{2}}$, b is the coefficient of x, c is the constant, and x is the variable.
Therefore, we will split the middle term that is bx in two terms which is equal to the sum of the factors of the product of the coefficient of ${{x}^{2}}$ and the constant, that is,
Let us suppose the two terms are p and q, therefore $p+q=b$ and $pq=ac$ . Thus, now we will substitute the sum of p and q in the place of middle term, we get
$a{{x}^{2}}+px+qx+c=0$
Therefore, we take a common term from the first two terms and another common term from the last two terms, to get the grouping factors in the form of linear polynomials.
Therefore, we can find the factors of the quadratic equation using the grouping method by splitting the middle term.

Note: While solving this problem, do not forget that after getting two groups, it must be in the form of linear polynomials. The name of solving this method is splitting the middle term method.