Find all rational zeros of the polynomial, and write the polynomial in factored form. P(x)=3x^{5}-14x^{4}-14x^{3}+36x^{2}+43x+10

Dolly Robinson

Dolly Robinson

Answered question

2021-05-20

Find all rational zeros of the polynomial, and write the polynomial in factored form.
P(x)=3x514x414x3+36x2+43x+10

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-05-22Added 93 answers

Step 1
Given polynomial is, P(x)=3x514x414x3+36x2+43x+10
By using rational root theorem,
11is the root of the expression, so factor out x+1.
3x514x414x3+36x2+43x+10x+1=3x417x3+3x2+33x+10
=(x+1)(x+1)(x2)(3x+1)(x5)
=(x+1)2(x2)(3x+1)(x5)
This is the factored form of the polynomial.
Step 2
and, the zeros are,
3x514x414x3+36x2+43x+10=0
(x+1)2(x2)(3x+1)(x5)=0
x+1=0 or x2=0 or 3x+1=0 or x5=0
x=1,x=2,x=13,x=5

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