Given px x 45x1x 23 State the zeros and their multiplicitie

Given p(x) = (x -4)^5(x+1)(x -2)^3 State the zeros and their multiplicities. What is the degree of the polynomial. Q11. Is x +2 a factor of the polynomial f(x) = x^3 -3x + 2? How do you know? Q12. Is x = 2 a zero of the polynomial x^3 -3x+2?Justify your answer. Q13. Graph the quadratic function f(x) = x^2 -6x+9 using its vertex, axis of symmetry, and intercepts. Choose the coned graph. Vertex (3,0) Vertex (3,9) Vertex (-3,0) Intercepts (0, 9), (3,0) Intercepts (0, 18) Intercepts (0,9), (-3,0) Q14. You have 100 feet oi fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Solution

Q10).

given

f(x) = (x-4)^5 . (x+1) .(x-2)^3

the degree of f(x)

For a polynomial with one variable (like x), the Degree is ...

... the largest exponent of that variable.

so here degree will be =

(x-4)^5 so 5

(x+1) so 1

(x-2)^3 so 3

degree = 5+1+3 =9

the zeros is x = 4,4,4,4,4 and x = -1 and x = 2,2,2

Q11)

given

f(x) = x^3 -3x+2

to check x+2 is a factor of f(x)

;et x+2=0

x=-2

plug x=-2 in f(x)

f(-2) = (-2)^3 -3(-2) +2

= -8 +6+2

= -8 +8

f(-2) =0 ( if this not zero , then we can x+3 is not a factor of f(x) )

so x+2 is a factor of f(x)   

Q12).

x=2 zero polynominal of f(x) =x^3 -3x+2

plug x=2

f(2) = (2)^3 -3(2) +2

f(2)= 8 -6+2

f(2) = 10 -6

f(2) =4

so

x=2 is not zero polynominal of f(x)