In this article, we will discuss the process of factorising a cubic polynomial in 2023. Factorising is a mathematical process which involves breaking down a polynomial into its individual components. A cubic polynomial is a type of polynomial that includes a power of three in its equation. It is one of the most common types of polynomials found in mathematics, and it can be used to solve a variety of equations. In this article, we’ll discuss the process of factorising a cubic polynomial in a simple and straightforward manner.

The basis of factorising a cubic polynomial involves understanding the concept of factors and terms. A factor is any number that, when multiplied by itself, produces a specific result. In the case of a cubic polynomial, the factors are numbers that, when multiplied together, produce the same result as the equation. The terms of a cubic polynomial are the individual parts of the equation that can be expressed in the form of a power of three. For example, the equation “x3 + 4×2 + 5x + 6” has five terms; x3, 4×2, 5x, and 6.

The process of factorising a cubic polynomial starts with identifying the factors of the equation. To do this, you must identify the three factors that, when multiplied together, will produce the same result as the equation. The factors of a cubic polynomial can be identified using a process called factoring by grouping. This process involves grouping the terms of the equation into two sets of parentheses, and then multiplying the terms inside each set together to produce the factors. For example, the equation “x3 + 4×2 + 5x + 6” can be factored by grouping the terms into two sets of parentheses: (x3 + 4×2) and (5x + 6). The factors of the equation are then found by multiplying the terms inside each set of parentheses together; in this case, the factors are 4x and 6.

Once the factors of the equation are found, the next step is to identify the terms of the equation that have the same power of three. For example, in the equation “x3 + 4×2 + 5x + 6”, the terms that have the same power of three are x3, 4×2, and 5x. This means that these terms can be factored out of the equation. To factor out the terms, you must divide each term by the same factor. For example, if the factor is 4x, then each term would be divided by 4x. The resulting equation would be “x3/4x + 4×2/4x + 5x/4x + 6/4x”. This equation can then be simplified to “x + x + 5/4 + 6/4”.

Once the equation has been simplified, the next step is to factor out the common factors from the equation. This is done by dividing each term by the same factor. For example, if the factor is x, then each term would be divided by x. The resulting equation would be “x + x + 5/x + 6/x”. This equation can then be simplified to “1 + 5/x + 6/x”. This equation can then be further simplified to “(1 + 5/x)(1 + 6/x)”, which is the factorised form of the equation.

Once the equation has been factorised, the next step is to identify the common factors of the equation. Common factors are numbers that can be used to solve the equation. For example, in the equation “(1 + 5/x)(1 + 6/x)”, the common factor is x. This means that if x is multiplied by both terms in the equation, the result will be the same as the original equation. In this example, the result would be “x3 + 4×2 + 5x + 6”.

Once the common factors of the equation have been identified, the next step is to simplify the equation as much as possible. This is done by dividing each term by the same factor. For example, if the factor is x, then each term would be divided by x. The resulting equation would be “1 + 5/x + 6/x”. This equation can then be further simplified to “(1 + 5/x)(1 + 6/x)”, which is the factorised form of the equation.

The final step in factorising a cubic polynomial is to identify the roots of the equation. The roots of the equation are the individual factors that, when multiplied together, produce the same result as the equation. To identify the roots, you must first identify the common factors of the equation. Once the common factors are identified, the roots can be determined by dividing each term by the same factor. For example, if the factor is x, then each term would be divided by x. The resulting equation would be “1 + 5/x + 6/x”. The roots of the equation are then found by solving for x in the equation; in this case, the roots are 5 and 6.

Factorising a cubic polynomial is a relatively simple process that can be used to solve a variety of equations. In this article, we’ve discussed the process of factorising a cubic polynomial in a simple and straightforward manner. We’ve also discussed the concept of factors and terms, as well as the process of factoring by grouping and simplifying equations. Finally, we’ve discussed the process of identifying the roots of the equation. By following the steps outlined in this article, you should be able to factorise a cubic polynomial with ease.