Examples on Factorization of Quadratic Equations
Example 1: Factorize: x2 – 5x + 6
Solution:
x2 – 5x + 6
⇒ x2 – 2x – 3x + 6
⇒ x(x – 2) – 3(x – 2)
⇒ (x – 2)(x – 3)
Example 2: Factorize: x2 – 6x + 9
Solution:
x2 – 6x + 9
⇒ x2 – 2.3x + (3)2
Comparing with a2 – 2ab + b2 = (a – b)2
⇒ (x – 3)2
Example 3: Factorize: x2 + x – 12
Solution:
x2 + x – 12
⇒ x2 +4x – 3x + 12
⇒ x(x + 4) – 3(x + 4)
⇒ (x + 4)(x – 3)
Example 4: Factorize: x2 + 8x + 16
Solution:
x2 + 8x + 16
⇒ x2 + 2.4x + (4)2
Comparing with a2 + 2ab + b2 = (a + b)2
⇒ (x + 4)2
Factorization of Quadratic Equations
Factorization of quadratic equation is another very important process in algebra which means breaking a quadratic equation into its linear factors. This technique is useful for solving quadratic equations, rewriting and simplifying algebraic expressions, or visualizing quadratic functions and their properties.
A quadratic equation is of the form of ax2 + bx + c= 0 with a, b, and c being real numbers or constants.
One way to perform it is by factorizing these equations so that it becomes easier to solve for them, and for more understanding of their roots and behaviors as well.
Table of Content
- What is Factorization of Quadratic Equations?
- Factorization Method of Quadratic Equations
- Factorization of Quadratic Equation by Splitting Middle Term
- Factoring Quadratic Equation using Formula
- Factoring Quadratic Equation using Quadratic Formula
- Factoring Quadratic Equations using Algebraic Identities
- Application of Factorization of Quadratic Equations