Question

Find a polynomial of the specified degree that has the given zeros. Degree 4; zeros −4, 0, 4, 6

Answer 1

Answer:

$P(x)=x^{4}-6x^{3}-16x^{2}+96x$

Step-by-step explanation:

1. The polynomial must have the following zeros:

$x=-4\\x=0\\x=4\\x=6$

2. This means the following:

$x+4=0\\x=0\\x-4=0\\x-6=0$

3. Multiply each term. The product of the multiplicaction is equal to zero. Then:

$(x+4)(x)(x-4)(x-6)=0$

4. $(x+4)$ and $(x-4)$ are conjugates, therefore, you have:

$(x^{2}-16)(x)(x-6)=0$

5. Apply the Distributive property. Then, you obtain:

$x^{4}-6x^{3}-16x^{2}+96x=0$

6. The polynomial of degree 4 and zeros −4, 0, 4 and 6 is:

$P(x)=x^{4}-6x^{3}-16x^{2}+96x$