# Math Help - Zeros and Multiplicity

1. ## Zeros and Multiplicity

For each polynomial function, state the zeros and the multiplicity.

(1) f(x) = 4(x + 4) [(x + 3)]^2

(2) f(x) = 4x(x^2 - 3)

2. Hello,
Originally Posted by magentarita
For each polynomial function, state the zeros and the multiplicity.

(1) f(x) = 4(x + 4) [(x + 3)]^2

(2) f(x) = 4x(x^2 - 3)
A number a is a zero of a polynomial if (x-a) divides the polynomial.
A number a is a zero of a polynomial, with multiplicity b if $(x-a)^b$ divides the polynomial.

It should be enough to do the exercise

3. ## Can you....

Originally Posted by Moo
Hello,

A number a is a zero of a polynomial if (x-a) divides the polynomial.
A number a is a zero of a polynomial, with multiplicity b if $(x-a)^b$ divides the polynomial.

It should be enough to do the exercise
Can you do the first one and I'll take it from there?

4. Originally Posted by magentarita
Can you do the first one and I'll take it from there?
Ok, but I would like you to show me how you do the second one then

$f(x)=4(x+4)(x+3)^2$

You can see that $(x+4)$ divides f(x). More exactly, if x=-4, you can see that x+4=0, that is to say f(-4)=0. Thus -4 is a zero.

What for x+3 ? If x=-3, x+3=0. Then f(-3)=0. -3 is a zero.

Now, what are their multiplicity ?
A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial.
The factor x+3 appears twice since it is $(x+3)^2=(x+3)(x+3)$. Its multiplicity is 2.

The factor (x+4) appears only once. Its multiplicity is 1.

5. ## Based on...........

Originally Posted by Moo
Ok, but I would like you to show me how you do the second one then

$f(x)=4(x+4)(x+3)^2$

You can see that $(x+4)$ divides f(x). More exactly, if x=-4, you can see that x+4=0, that is to say f(-4)=0. Thus -4 is a zero.

What for x+3 ? If x=-3, x+3=0. Then f(-3)=0. -3 is a zero.

Now, what are their multiplicity ?

The factor x+3 appears twice since it is $(x+3)^2=(x+3)(x+3)$. Its multiplicity is 2.

The factor (x+4) appears only once. Its multiplicity is 1.
Based on this reply, I should be able to find the zeros of similar polynomials.

Thanks

6. ## great

Originally Posted by Moo
Hello,

A number a is a zero of a polynomial if (x-a) divides the polynomial.
A number a is a zero of a polynomial, with multiplicity b if $(x-a)^b$ divides the polynomial.

It should be enough to do the exercise
What a great set of tips.

7. Thanks Moo!