15 Reasons Why Factoring Is Important?

No matter how hard you find it, factoring is a method of solving polynomial equations, and it is an important tool for simplifying and solving both linear and quadratic equations. Many people tend to opt out of factoring, considering it useless in practical life. This article shares some solid reasons explaining why factoring is important, so you start paying attention to those math classes:

15 Benefits of Factoring That Will Make You Want To Ace At It

Factoring numbers is the reverse process of multiplication. This article discusses 15 reasons explaining why factoring is important in math:

1. Factoring Helps To Speed Up Polynomial Long Division

You can use the factoring method to speed up polynomial long division. Polynomial long division method is not as fast as the factoring method. This is especially true when you have to perform multiple divisions by different divisors. Thus, it is important to understand the importance of factoring before using this algorithm for numerical operations.

2. Factoring Solves Linear Diophantine Equations

A Diophantine equation (named after Greek mathematician Diofantus) is an equation in which both sides are required to be integer values. Diophantine problems deal with finding integers that will satisfy the conditions of such equations.

Finding all non-negative integer solutions in a linear Diophantine equation can be done using the technique of factoring.

3. Factoring Helps Solve Quadratic Equations

Quadratic equations are important in different subjects such as calculus and geometry. In the context of calculus, quadratic equations can help find a slope or an area. In geometry, graph of a quadratic equation represents a parabola. According to mathematicians, factoring is the easiest way solving quadratic equation.

4. Factoring Helps Find Prime Factors Of A Number

Factoring helps find prime factors of a number which can help in performance rating calculation for nuclear reactors. Prime factorization of numbers is important to computer scientists and engineers who are involved in building cooling towers or bridges.

5. Factoring Helps Find The Greatest Common Factor

Factoring helps find the greatest common factor (GCF) of a number which is a very useful trick to solve problems in arithmetic and geometry. It also gives an insight into finding AC or GC of two numbers. This trick comes in handy to check if a given number is prime or composite.

6. Factoring Helps Find The Least Common Multiple (LCM)

Another important use of factoring is in finding the least common multiple (LCM). LCM can be particularly helpful in simplifying fractions and checking if two numbers are coprime (i.e., they have no factors in common). Factoring helps find LCM of a set of numbers or factorization of one number into its prime factors.

7. Factoring Helps Find The Least Common Denominator (LCD)

Another useful application of factoring is finding the least common denominator (LCD) of different fractions. It can be particularly helpful in simplifying fractions and finding equivalent fractions. It can also help you check if two numbers are coprime (i.e., they have no factors in common).

8. Factoring Is A Needed Skill In Schools

Factoring is one of the most important skills required to pass math tests, just like logic and science, especially at high school level. You can use it to find factors of a number or factorization of one number into its prime factors and do so much more of the basic math that you otherwise can never ace at.

9. Factoring Helps Create Perfect Squares

Factoring helps create perfect squares when you are given equation in the form x2 = b, where ‘b’ is an integer. It also helps when finding formula for quadratic equations like (x-h)2 = 4p or (x+h)2=4p to solve problems in geometry and algebra.

10. Factoring Makes Your Sharp

Using your brain to solve intricate stuff using factoring is a way to train your brain for sharpness. As you indulge in the complex task of solving equations, your brain is trained to become sharper and more analytical.

11. Factoring Helps Multiply Polynomials Using FOIL Method

One of the most important uses of factoring is multiplying polynomials using FOIL (First, Outer, Inner, Last) method. This method is extremely useful for simplifying long multiplication problems involving binomials and trinomials.

However, this method becomes time consuming and tedious when multiplying polynomials with a large number of terms. In such cases, you can use factoring to simplify these operations.

12. Factoring Helps To Solve Quadratic Equations Using The Quadratic Formula

There are several techniques proving that quadratic equations can be solved using the quadratic formula in case it is written in standard form (ax² + bx + c= 0). However, many people find this complicated for multiplying binomials when they are not written in standard form.

For instance, if you want to solve the equation 3 x2+ 7x-18=0, then there will be no issue when you have to use the quadratic formula. However, if it has to be solved in the form of (3x+6) (x-4)=0, then you will need some other technique. This is where factoring can help!

13. Factoring Helps Solve Inequalities Involving Monomials

In case you have been asked to solve inequalities involving monomials, factoring can be very helpful in these problems as it helps find roots from both positive and negative ends which you will need to use in the process of solving the inequality. This method will provide a better understanding of roots and their placement on number line as well as order of operations for complex rational expressions involving powers and root signs.

14. Factoring Helps Factor Trinomials Or Monomials

You can easily factor trinomials or monomial if they are written as ax2 + bx + c, where ‘a’ is a coefficient of x² term, ‘b’ is a coefficient of x term and ‘c’ is constant term. You can always use the standard form to simplify these types of expressions by identifying GCF first. This will ultimately help you to factor these expressions.

15. Factoring Helps Divide Polynomials Using The Quotient Algorithm

Another important application of factoring is dividing polynomials using quotient algorithm. This algorithm is helpful in simplifying most problems that require tedious steps for dividing polynomials. The most difficult part of this algorithm lies in finding the greatest common factor (GCF) of two numbers. However, once you’ve found it, rest of the process becomes super easy.

Why Factoring Is Important – Conclusion

There are several benefits that a student can gain from factorization. Most importantly, it will allow them to complete advanced mathematics problems with ease. Furthermore, it will also enhance their skills in arithmetic and algebra which might even help them get more jobs down the line. Thanks for reading.

References

https://www.britannica.com/science/factor-mathematics
https://study.com/academy/lesson/what-is-factoring-in-algebra-definition-example.html
https://www.mathsisfun.com/definitions/factoring.html