Zero Polynomials

Question

A Polynomial has a zero at -5, a double zero at 3 , and a zero at 6. Which of the following could be the polynomials described?

(x+5)(x-6)(x+3)

(x+5)(x-6)(x-3)

(x-5)(x+6)(x+3)^2

(x+5)(x-6)(x-3)^2

My teacher just taught this today and I would really like a step by step explanation to better understand this topic please

Answer 1

A Polynomial has a zero at -5, a double zero at 3 , and a zero at 6. Which of the following could be the polynomials described?

(x+5)(x-6)(x+3)

(x+5)(x-6)(x-3)

(x-5)(x+6)(x+3)^2

(x+5)(x-6)(x-3)^2

You want to know if you plug in the number (-5 or 3 or 6) that you will get a 0 result.

so if you plug in -5 for x

only the x + 5 will give you a 0, because -5 + 5 = 0

so you can eliminate the 3rd line.

next if you have a double zero at 3

only (x-3)^2 which is (x-3)(x-3) will give you a 0 twice, because 3-3 = 0 and 3-3 = 0

so you can eliminate lines 1 and 2

so this in your answer: (x+5)(x-6)(x-3)^2

Let me know how that helped, and give me an Up thumb so I know that you got it