Answer: x=−2,−3
Step-by-step explanation: 1. Factor the polynomial:
We can factor the polynomial using the sum-product pattern. This pattern states that the product of two numbers that add up to a and multiply to b is equal to x
2
+ax+b. In this case, we need to find two numbers that add up to 5 and multiply to 6. These numbers are 3 and 2.
x
2
+3x+2x+6
2. Extract the common factors:
We can now extract the common factors of x and (x+3):
x(x+3)+2(x+3)
3. Rewrite in factored form:
Finally, we can rewrite the expression in factored form:
(x+2)(x+3)
Answer:
The zeros of the equation are the values of x that make the factored expression equal to zero. Therefore, the zeros are:
x=−2,−3
In conclusion, the zeros of the quadratic equation x^2 + 5x + 6 are -2 and -3.
