To rewrite the quadratic equation [tex]\(x^2 + x - 12 = 0\)[/tex] in factored form, follow these steps:
1. Identify the quadratic equation: We start with the given quadratic equation:
[tex]\[
x^2 + x - 12 = 0
\][/tex]
2. Find two numbers that multiply to give the constant term (-12) and add to give the coefficient of the linear term (+1):
- We need two numbers whose product is [tex]\(-12\)[/tex] and whose sum is [tex]\(+1\)[/tex].
3. Determine the numbers: After checking possible pairs, we find that:
[tex]\[
4 \text{ and } -3
\][/tex]
satisfy the condition because [tex]\(4 \times -3 = -12\)[/tex] and [tex]\(4 + (-3) = 1\)[/tex].
4. Write the factors: The quadratic can thus be factored into two binomials:
[tex]\[
(x + 4)(x - 3)
\][/tex]
5. Write the entire equation: Since the original equation equaled zero, the factored form should also equal zero:
[tex]\[
(x + 4)(x - 3) = 0
\][/tex]
Hence, the quadratic equation [tex]\(x^2 + x - 12 = 0\)[/tex] in factored form is:
[tex]\[
(x + 4)(x - 3) = 0
\][/tex]
