Given P(x)=3x^{5}-x^{4}+81x^{3}-27x^{2}-972x+324, and that 6i is a zero, write P in factored form (as a product of linear factors). Be sure to write the full equation, including P(x)=.

Suman Cole

Suman Cole

Answered question

2021-08-02

Given P(x)=3x5x4+81x327x2972x+324, and that 6i is a zero, write P in factored form (as a product of linear factors). Be sure to write the full equation, including P(x)=.

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2021-08-03Added 97 answers

Step 1
P(x)=3x5x4+81x327x2972x+324
Given: 6i is a zero.
6i is also a zero.
(x+6i)(x6i) in a factor
(x2+36) in a factor of P(x).
Step 2
P(x)=3x5x4+81x327x2972x+324
=x4(3x1)+27x2(3x1)324(3x1)
=(3x1)(x4+27x2324)
=(3x1)[x2(x2+36)9(x2+36)]
=(3x1)(x2+36)(x29)
=(3x1)(x2+36)(x+3)(x3)
Factored form of P(x):
P(x)=(3x1)(x2+36)(x+3)(x3)

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