Complete Factorization. Factor the polynomial completely, and find all its

kzae220o3

kzae220o3

Answered question

2021-12-06

Complete Factorization. Factor the polynomial completely, and find all its zeros. State the multiplicity of each zero.
P(x)=x2+25

Answer & Explanation

Donald Proulx

Donald Proulx

Beginner2021-12-07Added 18 answers

Step 1
Given- P(x)=x2+25
To factor- The polynomial completely and find its all zero and state the multiplicity of each root.
Step 2
Explanation- Rewrite the given function,
P(x)=x2+25
To find the zeros of the any function, equate the above equation with zero and solving further, we get,
x2+25=0
x2i225=0 (since i2=1)
x2(i5)2=0
Now, factorising the above expression with using the formula (a2b2)=(ab)(a+b), we get,
(x-5i)(x+5i)=0
so, the roots of the above expression can be evaluated by solving further,
x=5i, -5i
So, the roots of the above function is 5i,-5i
Answer- Hence, the roots of the function P(x)=x2+25 is 5i, -5i and the multiplicity of each root is 1.

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