Find the complete factorization and all five zeros of the

Sam Longoria

Sam Longoria

Answered question

2021-12-08

Find the complete factorization and all five zeros of the polynomial
P(x)=3x5+24x3+48x

Answer & Explanation

Ethan Sanders

Ethan Sanders

Beginner2021-12-09Added 35 answers

Step 1
P(x)=3x5+24x3+48x
To find all the zeroes of the polynomial. Let, P(x)=0
0=3(x5+8x3+16x)
0=3x(x4+8x2+16)
0=3x(x4+4x2+4x2+16)
0=3x[x2(x2+4)+4(x2+4)]
0=3x[(x2+4)(x2+4)]
0=3x(x2+4)
Step 2
Therefore,
Zeroes of the polynomial are
x=0
x2+4=0 i.e. x2=4
i.e. x=±4
=±(i2×22)
=±2i
i.e.
x=2i and
x=-2i
Factorization of the polynomial is
3x(x2+4)2

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