Supply the numbers to write x² + 10x + 16 = 0 in it’s factored form. Enter the lesser number first.
The factored form of the quadratic equation x² + 10x + 16 = 0 is (x + 2)(x + 8). The lesser number is -8 and the greater number is -2. So, the factored form of the equation is (x + 8)(x + 2).
To write the quadratic equation x² + 10x + 16 = 0 in factored form, we can follow these steps:
Step 1: Identify the factors of the constant term (16) that can add up to the coefficient of the linear term (10). In this case, the factors of 16 are 1, 2, 4, 8, and 16. We can see that 2 and 8 add up to 10.
Step 2: Rewrite the quadratic equation using these factors as coefficients. Since the factors are 2 and 8, we have (x + 2)(x + 8) = 0.
Therefore, the factored form of the quadratic equation x² + 10x + 16 = 0 is (x + 2)(x + 8) = 0. The lesser number is -2 and the greater number is -8.
To factor the quadratic equation x² + 10x + 16 = 0, we need to find two numbers whose product is equal to 16, and whose sum is equal to 10 (the coefficient of the x term).
Let's break down the process step by step:
1. Write down the quadratic equation: x² + 10x + 16 = 0.
2. Determine the factors of 16:
The factors of 16 are 1 and 16, and 2 and 8, and -1 and -16, and -2 and -8.
3. Check if any of these factors add up to 10:
The only pair of factors that add up to 10 is 2 and 8.
4. Write the factored form:
To express x² + 10x + 16 in factored form, we use the factors we found:
(x + 2)(x + 8) = 0.
So, the factored form of the equation x² + 10x + 16 = 0 is (x + 2)(x + 8) = 0.