Find all rational zeros of the polynomial, and write the polynomial in factored form. P(x)=6x^{4}-23x^{3}-13x^{2}+32x+16

e1s2kat26

e1s2kat26

Answered question

2021-04-06

Find all rational zeros of the polynomial, and write the polynomial in factored form.
P(x)=6x423x313x2+32x+16

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-04-08Added 91 answers

Step 1
Given polynomial is, P(x)=6x423x313x2+32x+16.
The zeroes are found as follows:
6x423x313x2+32x+16
6x3(x+1)29x2(x+1)+16x(x+1)+16(x+1)=0
(x+1)(6x329x2+16x+16)=0
(x+1)(2x+1)(3x216x+16)=0
(x+1)(x-4)(2x+1)(3x-4)=0
Step 2
On solving further,
x+1=0 or x-4=0 or 2x+1=0 or 3x-4=0
x=1,x=4,x=12,x=43
Thus, rational zeroes are 12 and 43. And, the factored form of the polynomial is (x+1)(x-4)(2x+1)(3x-4).

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