Answer:
.
Step-by-step explanation:
Apply the quadratic formula to find all factors. For a quadratic equation in the form
,
where , , and are constants, the two roots will be
, and
.
For this quadratic polynomial,
Apply the quadratic formula to find any value or values that will set this polynomial to zero:
.
.
Apply the factor theorem to find the two factors of this polynomial:
- for the root , and
- for the root .
Keep in mind that simply multiplying the two factors will not reproduce the original polynomial. Doing so assumes that the leading coefficient of in the original polynomial is one, which isn't the case for this question.
Multiply the product of the two factors by the leading coefficient of in the original polynomial.
.
Expand to make sure that the factored form is equivalent to the original polynomial:
.