All the real zeros of the given polynomial are integers.

Mary Jackson

Mary Jackson

Answered question

2021-12-14

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
P(x)=x319x30

Answer & Explanation

Archie Jones

Archie Jones

Beginner2021-12-15Added 34 answers

Step 1
P(x)=x319x30
To find the zeroes of the polynomial, put P(x) = 0
i.e.
0=x319x30
0=x3+0x219x30
0=x3+3x23x29x10x30
0=x2(x+3)3x(x+3)10(x+3)
0=(x23x10)(x+3)
0=(x25x+2x10)(x+3)
0=[x(x-5)+2(x-5)](x+3)
0=(x+2)(x-5)(x+3)
Step 2
y=0 at
x=-2,
x=5
and x=-3
In the factored form:
P(x)=(x+2)(x-5)(x+3)
Jenny Sheppard

Jenny Sheppard

Beginner2021-12-16Added 35 answers

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