Question

Form a polynomial whose zeros and degree are given.
Zeros: 2, multiplicity 2; 3, multiplicity 1; degree 3

A. x^3+7x^2+16x+12
B. x^3+7x^2+12x+12
C. x^3-4x^2+16x-12
D. x^3-7x^2+16x-12

Answer 1

So we're given that are zeros/roots are:
2 with a multiplicity 2
3 with a multiplicity 1

In other words, our roots are 2, 2, 3!

Working backwards, we see that if those are the roots, then that means that
x=2, x=2, and x=3
x-2=0, x-2=0, x-3=0
(x-2)(x-2)(x-3)=0

Now multiply those terms and you'll get your answer!

Answer 2

What terms do you multiply??

Answer 3

(x-2)(x-2)(x-3)

Answer 4

so the answer would be, x^3-3x^2+4x-12?

Answer 5

But that's not one of my answers...

Answer 6

You're probably made a mistake when you were solving algebraically.
(x-2)(x-2)(x-3)
(x-2)^2 (x-3)
(x^2-4x+4)(x-3)

Is this what I have so far? Do you understand how I got there?

Answer 7

you*

Answer 8

yes i got that.