Question

If p(x) is a polynomial that has a simple zero at x=-3 and a double zero at x= 5/4, then which of the following could be the factored for of p(x)?

A) p(x)=2(x+3)(5x-4)
B) p(x)=(x+3)(5x-4)²
C) p(x)=2(x+3)(4x-5)
D) p(x)=(x+3)(4x-5)²

Answer 1

D

Explanation:

x=-3 is a zero means x+3 is a factor

x=5/4 (with multiplicity 2) means you have the factor (x-5/4) two times

Now this may be rewritten so you don't have the fraction

like 4x=5 so you have 4x-5 as a factor two times which means you will see (4x-5)^2

So you one factor of (x+3) and two factors of (4x-5)

so you have

(x+3)(4x-5)^2

or

2(x+3)(4x-5)^2

or

41(x+3)(4x-5)^2

You can put whatever constant multiple in front of the whole thing and it will still satisfy the conditions of the problem.

So the answer is D