All the real zeros of the given polynomial are integers.

hadejada7x

hadejada7x

Answered question

2021-12-10

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
P(x)=x3+11x2+8x20

Answer & Explanation

Jillian Edgerton

Jillian Edgerton

Beginner2021-12-11Added 34 answers

Step 1
Given polynomial function is:
P(x)=x3+11x2+8x20
We have to find all the zeroes of the above polynomial and write the polynomial in factored form.
Step 2
Then we get,
P(x)=x3+11x2+8x20
P(x)=x3+10x2+x2+8x20
P(x)=(x3+10x2)+(x2+8x20)
P(x)=x2(x+10)+(x+10)(x2)
P(x)=(x+10)(x2+x2)
P(x)=(x+10)(x+2)(x1)
Hence all the real zeroes of this polynomial are:
x = -10 ; x = -2 ; x = 1
The factored form of the given polynomial is:
P(x)=(x-1)(x+2)(x+10)
Hence the answer.

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