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HomeNY Regents Algebra IIMathematicsGraphs of Polynomial Functions › For f(x) = (x + 2) cubed times (x - 5) squared t…

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_
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