Find all rational zeros of the polynomial, and write the polynomial in factored form. P(x)=4x^{4}-37x^{2}+9

EunoR 2021-05-04 Answered
Find all rational zeros of the polynomial, and write the polynomial in factored form.
P(x)=4x437x2+9
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Expert Answer

komunidadO
Answered 2021-05-06 Author has 86 answers

Step 1
Given, P(x)=4x437x2+9
For zeroes, substituting,P(x)=0
4x437x2+9=0
4x436x2x2+9=0
4x2(x29)(x29)=0
(x29)(4x21)=0
(x232)((2x)21)=0
(x+3)(x3)(2x+1)(2x1)=0
(Using,(a2b2)=(a+b)(ab))
(x+3)=0, or, (x-3)=0, or , (2x+1)=0, or, (2x-1)=0
x=3,3,12,12
Hence, zeroes are: x=(3,12,12,3).
Step 2
Required factorized form is:
4x437x2+9=(x+3)(x3)(2x+1)(2x1)

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