Find the polynomial of the specified degree that has the

eliaskidszs

eliaskidszs

Answered question

2022-01-15

Find the polynomial of the specified degree that has the given zeros. the coefficient of the leading term is 1. assume a=1 and make sure to expand f(x) all the way no parentheses
degree 3; zeros -3, -1, 2 also write the polynomial in expanded form

Answer & Explanation

movingsupplyw1

movingsupplyw1

Beginner2022-01-16Added 30 answers

Step 1
As we know that the polynomial of order n having a leading coefficient a with zeros c1,c2,c3..cn is given by,
p(x)=a(xc1)(xc2)(xc3)(xcn)
Step 2
Given, the leading coefficient a=1, n=3 and c1=3,c2=1 and c3=2, then the polynomial in the factored form is:
p(x)=1(x-(-3)x-(-1)(x-2))
p(x)=(x+3)(x+1)(x-2)
Now expand the polynomial,
p(x)=(x2+x+3x+3)(x2)
p(x)=(x2+4x+3)(x2)
p(x)=x32x2+4x28x+3x6
p(x)=x3+2x25x6
Therefore, the polynomial is:
p(x)=x3+2x25x6
Andrew Reyes

Andrew Reyes

Beginner2022-01-19Added 24 answers

Given data,
degree = 3
zeros =-3, -1,2
leading coefficient = 1
f(x)=1(x+3)(x+1)(x-2)
multiply the each term with another term in equation.
(x+3)(x+1)(x2)
(x2+x+3x+3)(x2)
x32x2+x22x+3x26x+3x6
write same type of term at one place
x3+4x22x28x+3x6
x3+32x25x6
\therefore polynomial expanded form
f(x)=x3+2x25x6

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