Consider the polynomial function p(x)=(3x^{2}-5x-2)(x-5)(x^{2}-4). A) what is the degree of the polynomial? What is the y intercept of the function? B

geduiwelh

geduiwelh

Answered question

2021-05-11

Consider the polynomial function p(x)=(3x25x2)(x5)(x24).
A) what is the degree of the polynomial? What is the y intercept of the function?
B)What are the zeros and their multiplicities?
C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?

Answer & Explanation

Bella

Bella

Skilled2021-05-12Added 81 answers

Step 1
Given:
p(x)=(3x25x2)(x5)(x24)
Step 2
Now,
(A):
The degree of the polynomial is 5.
y-intercept is when x=0.
So,
p(0)=(-2)(-5)(-4)=-40
Hence y-intercept is (0,-40).
(B):
(3x25x2)(x5)(x24)=0
(3x26x+x2)(x5)(x+2)(x2)=0
(3x+1)(x-2)(x-5)(x+2)(x-2)=0
(3x+1)(x5)(x+2)(x2)2=0
x=13,x=5,x=2,x=2
So, the zeros are: 13,5,-2,2 (with multiplicity 2).
(C) By multiplying the expression with each other, we get the leading term of the polynomial =3x4.

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