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

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

Ethan Sanders · Accepted Answer

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

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

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