Respuesta :
The complete question is;
The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____
Answer:
A) degree = 6
B) -9 is also a zero of the polynomial
C) 0 has multiplicity of 2
1 has multiplicity of 3
Step-by-step explanation:
A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.
The terms are;
5x², (x - 1)³, (x + 9)
The exponents are, 2, 3 and 1 respectively.
Thus, degree = 2 + 3 + 1 = 6
B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.
Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².
Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³
Thus,we are left with the term (x + 9)
So for the polynomial to be zero, (x + 9) = 0
Thus,x = -9
So -9 is a zero of the polynomial
C) The zero 0 is from the term 5x².
Thus,the multiplicity is the highest power of x which is 2.
The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3
