How To Factorise 2X² + 5X + 3

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Introduction

In mathematics, factorisation is the process of breaking down an expression into its constituent parts. It is an important skill in algebra that helps simplify and solve equations. In this article, we will be discussing how to factorise the expression 2x² + 5x + 3.

Step 1: Identify the Factors of the First and Last Terms

To begin factorising, we first need to identify the factors of the first and last terms of the expression. In this case, the first term is 2x², which can be factored as 2x × x, and the last term is 3, which can be factored as 1 × 3 or 3 × 1.

Step 2: Find the Factors That Add Up to the Middle Term

Next, we need to find the factors of the middle term, which is 5x, that add up to the middle coefficient. In this case, the only two factors of 5x are 1x and 5, which add up to 6x, not 5x. Therefore, we need to use different factors.

Step 3: Trial and Error Method

One method to find the factors that add up to the middle term is the trial and error method. We can list all possible factor pairs of 2x² and 3 and check which pair adds up to 5x. The factor pairs of 2x² are: - 2x × x - (-2x) × (-x) The factor pairs of 3 are: - 3 × 1 - (-3) × (-1) We can then test each pair by multiplying them and checking if they add up to 5x. After some trial and error, we can see that the factors that add up to 5x are 2x and 3.

Step 4: Write the Factors in Parentheses

Once we have found the correct factors, we can write them in parentheses. The expression then becomes: 2x² + 5x + 3 = (2x + 3)(x + 1)

Step 5: Check the Answer

To check if the factorisation is correct, we can use the distributive property to expand the expression back to its original form: (2x + 3)(x + 1) = 2x² + 3x + 2x + 3 = 2x² + 5x + 3 The expanded form is the same as the original expression, so our factorisation is correct.

Conclusion

Factorising is an essential skill in algebra that allows us to simplify expressions and solve equations. By following the steps outlined in this article, we can factorise the expression 2x² + 5x + 3 using the trial and error method. It is important to check our answer by expanding the expression back to its original form.