What polynomial has roots of -4, 1, and 6

a.x3 - 3x2 - 22x + 24

b.x3 - x2 - 26x - 24

c.x3 + x2 - 26x + 24

d.x3 + 3x2 + 14x - 24

Question

What polynomial has roots of -4, 1, and 6

a.x3 - 3x2 - 22x + 24
 		
b.x3 - x2 - 26x - 24
 		
c.x3 + x2 - 26x + 24
 		
d.x3 + 3x2 + 14x - 24

jdoe0001 · Answer

multiply the roots and expand

-4  => x= -4  =>  x+4 = 0   => (x+4)  as the root
1   => x = 1    => x-1   = 0   => (x-1) as the root
....

anonymous · Answer

similar to what i started writing

anonymous · Answer

@jdoe0001 can you explain a little bit further?

anonymous · Answer

@tkhunny that was kind of interesting, where did you learn that trick?

anonymous · Answer

so b?

anonymous · Answer

Be a little careful. In your example, the last term is (-a)(-b)(-c)(-d), and the negatives cancel out. Will that happen in our problem?

tkhunny · Answer

Be a LOT more careful.  Not sure how I talked myself into that.

Once we have the FACTORS from the ROOTS, THEN it's as obvious as I said.

Root
-4
1
6

Factor
x - (-4) = x+4
x - 1
x - 6

Now, (+4)(-1)(-6) = +24 and immediately discard B and D.

Yikes, time for a break.

anonymous · Answer

Basically, the fact that -4, 1, and 6 are roots of this polynomial tell us that:$$(x-(-4))(x-1)(x-6)$$is the polynomial we are after. Your job is to multiply this all together. That will give you the answer.

anonymous · Answer

Note this is the same as:$$(x+4)(x-1)(x-6)$$

anonymous · Answer

@joemath314159 alright, alright, I can understand what you saying :) thanks a lot!