Factorise the expression 6x2 + 11x + 4.

Step 1: Factorise the expression 6x^2 + 11x + 4. To factorise the quadratic expression ax^2 + bx + c, we look for two numbers that multiply to a × c and add up to b. Here, a=6, b=11, c=4. So, we need two numbers that multiply to 6 × 4 = 24 and add up to 11. These numbers are 3 and 8. We rewrite the middle term 11x as 3x + 8x. 6x^2 + 11x + 4 = 6x^2 + 3x + 8x + 4 Now, we factor by grouping. 3x(2x + 1) + 4(2x + 1) Factor out the common binomial (2x + 1). (3x + 4)(2x + 1) The factorised expression is (3x + 4)(2x + 1). Step 2: Identify the dimensions of the garden. The area of a rectangle is given by length × width. Since the area is represented by the expression 6x^2 + 11x + 4, and we factorised it into (3x + 4)(2x + 1), the dimensions are the factors. The dimensions of the garden are 3x + 4 and 2x + 1. Step 3: Calculate the actual dimensions and area if x = 2 metres. Substitute x = 2 into the expressions for the dimensions: Length: 3(2) + 4 = 6 + 4 = 10 metres. Width: 2(2) + 1 = 4 + 1 = 5 metres. The actual dimensions are 10 metres and 5 metres. Now, calculate the actual area: Area = Length × Width = 10 m × 5 m = 50 m^2. The actual area of the garden is 50 m^2. Step 4: Explain the usefulness of factorisation in real-world problems. Factorisation is useful because it allows us to break down a complex expression (like the total area) into its simpler components (like the length and width of the garden). This helps in understanding the individual parts of a problem, which is essential for planning, design, and making practical calculations in real-world scenarios. Send me the next one 📸