How To Factorise X^2 + 5X + 4

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Introduction

In mathematics, factorisation is the process of breaking down a polynomial expression into its factors. Factorisation is an important skill that is required in algebra and calculus, and it is used to simplify complex equations, solve problems, and find solutions. In this article, we will discuss how to factorise the polynomial expression x^2 + 5x + 4.

Step 1: Identify the Factors of the Constant Term

To factorise x^2 + 5x + 4, we first need to identify the factors of the constant term, which is 4. The factors of 4 are 1, 2, and 4. We will use these factors in the next step.

Step 2: Find a Pair of Factors that Add up to the Coefficient of x

Next, we need to find a pair of factors that add up to the coefficient of x, which is 5. We can do this by trial and error or by using the following formula: a + b = 5 ab = 4 By solving this system of equations, we can find that the pair of factors is 1 and 4.

Step 3: Rewrite the Polynomial Expression

Now that we have identified the factors of the constant term and a pair of factors that add up to the coefficient of x, we can rewrite the polynomial expression as follows: x^2 + 5x + 4 = (x + 1)(x + 4)

Step 4: Check the Solution

To check if the factorisation is correct, we can use the distributive property of multiplication and expand the expression: (x + 1)(x + 4) = x(x + 4) + 1(x + 4) = x^2 + 4x + x + 4 = x^2 + 5x + 4 Therefore, the factorisation is correct.

Conclusion

In conclusion, factorisation is an important skill in mathematics that is used to simplify complex equations and find solutions. To factorise x^2 + 5x + 4, we need to identify the factors of the constant term and find a pair of factors that add up to the coefficient of x. By following these steps, we can rewrite the polynomial expression as (x + 1)(x + 4). It is important to check the solution by expanding the expression and verifying that it equals the original polynomial.