Algebraic expressions with more than one term can be difficult to simplify or solve. However, factorising can help us to break down the expression into simpler terms which makes it easier to solve. In this article, we will learn how to factorise the expression 2x² + 7x + 3.
Factorising the Expression
To factorise, we need to find two numbers that multiply to give the constant term (3) and add up to give the coefficient of the middle term (7). These numbers are 1 and 3. We can rewrite the expression as follows: 2x² + 7x + 3 = 2x² + 3x + 4x + 3 Now, we group the terms as follows: 2x(x + 3) + 1(4x + 3) We can see that we have a common factor of (x + 3) in the first group and a common factor of (4x + 3) in the second group. Therefore, we can factorise the expression as follows: 2x² + 7x + 3 = (2x + 1)(x + 3)
Checking the Factorisation
To check if our factorisation is correct, we can expand the brackets and simplify the expression. If we get back the original expression, then our factorisation is correct. Let's expand the brackets: (2x + 1)(x + 3) = 2x(x + 3) + 1(x + 3) = 2x² + 6x + x + 3 = 2x² + 7x + 3 We can see that we have obtained the original expression, which means that our factorisation is correct.
Applications
Factorising can be helpful in solving quadratic equations, simplifying algebraic expressions, and finding common factors. It is an important skill in algebra and is used in many fields such as physics, engineering, and finance.
Conclusion
In this article, we have learned how to factorise the expression 2x² + 7x + 3. We found two numbers that multiply to give the constant term and add up to give the coefficient of the middle term. We then grouped the terms and factorised the expression. We checked our factorisation by expanding the brackets and simplifying the expression. Factorising is an important skill in algebra and has many applications in various fields.
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