even multiplicity - If y = (x-1)^{4} (x+5) (x-2)^{3} is a polynomial function. Which of the roots of the polynomial have a odd multipliity and an even multiplicity?

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what is a polynomial

STEP 2: Recall what are the roots of a polynomial

STEP 3: What is multiplicity of a polynomial

STEP 4: Write which of the roots have even and odd multiplicity

Since the exponent of the term (x-1) is 4. The root x = 1 has an even multiplicity

Since the exponent of the term (x+5) is 1, the root x = -5 has an odd multiplicity

Since the exponent of the term (x-2) is 3, the root x = 2 has an odd multiplicity

Further skills to recall:

What are exponents

What are terms in a polynomial