Write a polynomial, P(x), in factored form given the following

hadejada7x

hadejada7x

Answered question

2021-12-26

Write a polynomial, P(x), in factored form given the following requirements.
Degree: 3
Zeros at (8,0), (2,0), and (−5,0)
y-intercept at (0,80).

Answer & Explanation

xandir307dc

xandir307dc

Beginner2021-12-27Added 35 answers

Step 1
here given zeros are x=8, x=2, x=-5
so the factored form is
f(x)=a(x8)(x2)(x+5)...(1)
here y-interest is (0,80)
80=a(0-8)(0-2)(0+5)
80=a(-8)(-2)(5)
80=a*80
a=1...put it back in equation 1
Step 2
f(x)=a(x-8)(x-2)(x+5)
f(x)=1(x-8)(x-2)(x+5)
f(x)=(x-8)(x-2)(x+5)
f(x)=(x28x2x+16)(x+5)
f(x)=(x210x+16)(x+5)
f(x)=x310x2+16x+5x250x+80
f(x)=x35x234x+80
Jenny Sheppard

Jenny Sheppard

Beginner2021-12-28Added 35 answers

Given, Degree: 3
Zeroes, (8,0),(2,0), and (-5,0)
y-intercept at (0,80)
so,
(x-8)(x-2)(x+5)=0
(x28x2x+16)(x+5)=0
(x210x+16)(x+5)=0
x3+5x210x250x+16x+80=0
x35x234x+80=0
So, P(x)=x35x234x+80
Vasquez

Vasquez

Expert2022-01-09Added 669 answers

Equation of polynomial is factored form is
f(x)=a(x8)(x2)(x(5))
f(x)=a(x8)(x2)(x+5)
Given at x=0 f(0)=80
a(08)(02)(0+5)=80a(8)(2)(5)=8080a=80a=1
So, f(x)=(x-8)(x-2)(x+5)

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