Factorise the quadratic expression below: 𝑥2+10𝑥+21x 2 +10x+21

Sure, here are the steps to factorise the quadratic expression x² + 10x + 21:

1. Identify the coefficients in the quadratic expression. In this case, a = 1 (coefficient of x²), b = 10 (coefficient of x), and c = 21 (constant term).

2. Look for two numbers that multiply to give ac (in this case, 121 = 21) and add up to give b (in this case, 10). The numbers that satisfy these conditions are 7 and 3 because 73 = 21 and 7 + 3 = 10.

3. Rewrite the middle term of the quadratic expression as the sum of the terms 7x and 3x. This gives us x² + 7x + 3x + 21.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x² + 7x) + (3x + 21).

5. Factor out the greatest common factor from each group. From the first group, we can factor out x to get x(x + 7). From the second group, we can factor out 3 to get 3(x + 7).

6. Now, you can see that (x + 7) is a common factor. Factor this out to give the final answer: (x + 7)(x + 3).

So, the factorised form of the quadratic expression x² + 10x + 21 is (x + 7)(x + 3).