convert y=x^2+9x+14 to factored form
(x+7)(x+2)
To convert the quadratic equation y = x^2 + 9x + 14 to factored form, we need to express it as a product of its factors. Here's how you can do it step by step:
Step 1: Write down the equation: y = x^2 + 9x + 14
Step 2: Look for two numbers whose sum is 9 (coefficient of the x term) and whose product is 14 (constant term).
In this case, we need to find two numbers that add up to 9 and multiply to 14. The numbers that fit these criteria are 2 and 7.
Step 3: Rewrite the equation by splitting the middle term using the two numbers: y = x^2 + 2x + 7x + 14
Step 4: Group the terms: y = (x^2 + 2x) + (7x + 14)
Step 5: Factor out the greatest common factor from each group: y = x(x + 2) + 7(x + 2)
Step 6: Notice that both groups have a common factor of (x + 2), so we can factor out (x + 2): y = (x + 2)(x + 7)
Therefore, the factored form of the quadratic equation y = x^2 + 9x + 14 is (x + 2)(x + 7).