Factorise 𝑥2+2𝑥−15

Sure, here is the step-by-step solution to factorize the quadratic equation 𝑥² + 2𝑥 - 15:

Step 1: Identify the coefficients of the quadratic equation. Here, a = 1, b = 2, and c = -15.

Step 2: Find two numbers that multiply to give ac (a times c), and add to give b. In this case, we need two numbers that multiply to -15 and add to 2. The numbers 5 and -3 fit these criteria because 5 * -3 = -15 and 5 + -3 = 2.

Step 3: Rewrite the middle term of the quadratic equation (the term involving x) as the sum of the terms involving the two numbers found in step 2. This gives us 𝑥² + 5𝑥 - 3𝑥 - 15.

Step 4: Factor by grouping. This involves factoring out common factors from the first two terms and the last two terms separately. For the first two terms, the common factor is x, and for the last two terms, the common factor is -3. This gives us x(𝑥 + 5) - 3(𝑥 + 5).

Step 5: Notice that (𝑥 + 5) is a common factor of both terms. Factor out (𝑥 + 5), which gives us (𝑥 + 5)(𝑥 - 3).

So, 𝑥² + 2𝑥 - 15 factorizes to (𝑥 + 5)(𝑥 - 3).