Answer:
Degree: 5
Y-intercept: 12
Step-by-step explanation:
The given expression is
[tex]f(x)=-(x+1)^2(2x-3)(x+2)^2[/tex]
Since the factors are multiplying, we can analyse the degree of each factor and add them to find the degree of the polynomial.
The degree of the factor [tex]-(x+1)^2[/tex] is 2.
The degree of [tex](2x-3)[/tex] is 1
The degree of [tex](x+2)^2[/tex] is 2
Therefore the degree of the polynomial is 2+1+2=5
To find the y-intercept, we put x=0.
[tex]f(0)=-(0+1)^2(2(0)-3)(0+2)^2[/tex]
[tex]f(0)=-(-3)(4)=12[/tex]
The y-intercept is 12
