The quadratic equation x^2 + 4x - 32 = 0 can be solved by factoring.Which of the following is the factored form?
A. (x + 8) (x - 4) = 0
B. (x + 4) (x + 8) = 0
C. (x + 4) (x - 8) = 0
D. (x - 4) (x - 8) = 0
The factored form of the quadratic equation x^2 + 4x - 32 = 0 is:
(x + 8)(x - 4) = 0
Therefore, the correct answer is A. (x + 8) (x - 4) = 0.
To solve the equation x^2 + 4x - 32 = 0 by factoring, we need to find two binomials that, when multiplied together, give us the quadratic equation.
First, we need to find two numbers whose product is -32 and whose sum is 4.
The factors of 32 are: 1, 2, 4, 8, 16, 32.
By trying different combinations, we find that -4 and 8 satisfy the conditions since -4 * 8 = -32 and -4 + 8 = 4.
Therefore, the factored form of the quadratic equation is (x - 4)(x + 8).
So, the correct answer is option D: (x - 4)(x - 8) = 0.
To solve a quadratic equation by factoring, we need to find two binomials whose product is equal to zero.
For the given quadratic equation x^2 + 4x - 32 = 0, we need to find two binomials that, when multiplied together, give us zero.
To factor this equation, we need to find two numbers whose sum is equal to the coefficient of the middle term (4), and whose product is equal to the constant term (-32).
First, let's find the factors of -32: -1, 1, -2, 2, -4, 4, -8, 8, -16, and 16.
Now, let's check which pair of factors have a sum of 4:
-1 + 32 = 31 (not a solution)
1 + (-32) = -31 (not a solution)
-2 + 16 = 14 (not a solution)
2 + (-16) = -14 (not a solution)
-4 + 8 = 4 (yes, this pair works!)
So, the two binomials that can be multiplied together to get zero are (x - 4) and (x + 8).
Therefore, the factored form of the quadratic equation x^2 + 4x - 32 = 0 is:
(x - 4)(x + 8) = 0
Hence, the correct answer is option B.