Solving Quadratic Equations Using Patterns Quick Check

Question

1 of 51 of 5 Items
Question
The quadratic equation x2+4x−32=0 can be solved by factoring. Which of the following is the factored form?(1 point)
Responses

(x+8)(x−4)=0
left parenthesis x plus 8 right parenthesis left parenthesis x minus 4 right parenthesis equals 0

(x+4)(x−8)=0
left parenthesis x plus 4 right parenthesis left parenthesis x minus 8 right parenthesis equals 0

(x+4)(x+8)=0
left parenthesis x plus 4 right parenthesis left parenthesis x plus 8 right parenthesis equals 0

(x−4)(x−8)=0
left parenthesis x minus 4 right parenthesis left parenthesis x minus 8 right parenthesis equals 0

Answer 1

To factor the quadratic equation \( x^2 + 4x - 32 = 0 \), we need to look for two numbers that multiply to \(-32\) (the constant term) and add to \(4\) (the coefficient of \(x\)).

The two numbers that fit this requirement are \(8\) and \(-4\) because:

• \(8 \times (-4) = -32\)
• \(8 + (-4) = 4\)

Thus, the factored form of the equation is:

\[ (x + 8)(x - 4) = 0 \]

So, the correct response is:

\[ (x+8)(x−4)=0 \]