All the real zeros of the given polynomial are integers. Find the zeros, and write...

Madeline Lott

Madeline Lott

Answered

2021-12-19

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
P(x)=x34x219x14

Answer & Explanation

Durst37

Durst37

Expert

2021-12-20Added 37 answers

Step 1
Given polynomial is, P(x)=x34x219x14
In factored form, it is written as follows:
x34x219x14=x3+x25x25x14x14
=x2(x+1)5x(x+1)14(x+1)
=(x+1)(x25x14)
=(x+1)(x(x+2)-7(x+2))
=(x+1)(x+2)(x-7)
Step 2
It zeroes are find by putting it equal to zeros.
x34x219x14=0
(x+1)(x+2)(x-7)=0
x+1=0 or x+2=0 or x-7=0
x=-1, x=-2, x=7
Ella Williams

Ella Williams

Expert

2021-12-21Added 28 answers

P(x)=x34x219x14
rational roots of the function are
x=+-{1,2,7,14}
actual roots occur at
x = -1 , -2 , 7
hence zeros are
x = -1 , -2 , 7
polynomial in factored form is
P(x) = (x+1) ( x+2) (x-7)

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