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For f(x) = (x + 2) cubed times (x - 5) squared times (x - 1), what is the degree?
ADegree 3
BDegree 5
CDegree 6
DDegree 9
Answer & Solution
Correct answer: C. Degree 6
1. Each bracket contributes a zero whose multiplicity is the power on that bracket.
2. The bracket (x + 2) is cubed, giving multiplicity 3.
3. The bracket (x - 5) is squared, giving multiplicity 2.
4. The bracket (x - 1) has no written power, so its multiplicity is 1.
5. The sum of the multiplicities is the degree, so add 3 plus 2 plus 1.
6. That gives a degree of 6.
7. Degree 3 takes only the largest multiplicity instead of the total.
8. Degree 5 leaves out the unwritten power of 1 on the last bracket.
9. Degree 9 multiplies 3 by 3 rather than adding the three multiplicities.
_Source: OpenStax Precalculus (CC BY 4.0), section 3.4 Graphs of Polynomial Functions_