Jonathan is making his favorite pasta dish. He serves his mom 1/12 of the pot of pasta and his brother 1/6 of the pot. How much
2 answers:
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Answer:
Choice b.
.
Step-by-step explanation:
The highest power of the variable in this polynomial is
. In other words, this polynomial is quadratic.
It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to .)
After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.
Apply the quadratic formula to find the two roots that would set this quadratic polynomial to . The discriminant of this polynomial is
.
.
Similarly:
.
By the Factor Theorem, if is a root of a polynomial, then
would be a factor of that polynomial. Note the minus sign between
and
.
- The root
corresponds to the factor
, which simplifies to
.
- The root
corresponds to the factor
, which simplifies to
.
Verify that indeed expands to the original polynomial:
.