1. ## Polynomial Functions

Can anyone help me solve this question..its urgent ^^ thank you

For each of the following polynomial functions, determine if each of x=-1, x=0 and/or x=2 is a zero of the polynomial and, if so, whether its muliplicity is even or odd.

1.) f(x)= x^4+2x^3+2x^2
2.) g(x)=5x^2-5x-10
3.) h(x)= x^3(x+1)^4(x+2)
4.) The graph of p(x) is :

2. Originally Posted by lemontea
Can anyone help me solve this question..its urgent ^^ thank you

For each of the following polynomial functions, determine if each of x=-1, x=0 and/or x=2 is a zero of the polynomial and, if so, whether its muliplicity is even or odd.

1.) f(x)= x^4+2x^3+2x^2
2.) g(x)=5x^2-5x-10
3.) h(x)= x^3(x+1)^4(x+2)
4.) The graph of p(x) is :
multiplicity just tells you how many times a root is "repeated".

for instance, if we had a quadratic of the form $\displaystyle (x - 2)^2$, the only root would be $\displaystyle x = 2$, since this makes the quadratic zero. but, a quadratic must have two roots. so there should be one more, but low and behold! the square tells us the root is repeated a second time. so $\displaystyle x = 2$ is a root with multiplicity 2

note that $\displaystyle f(x) = x^2 (x^2 + 2x + 2)$

what x's make this zero?

note that $\displaystyle g(x) = 5(x^2 - x - 2) = 5(x - 2)(x + 1)$

what x's make this zero?

h(x) is already in a nice factored form, what x's make it zero? the powers tell you the multiplicity

for p(x), look at the graph. wherever the graph touches the x-axis, that is a root. if it passes through, the multiplicity is 1, if there is a hump and the graph touches the x-axis without cutting it, the multiplicity is 2.