Question

Which of the following is the factorization of x^3 - 5x^2 - 16x + 80.

a. (x-4)(x+4)(x+5)
b.(x-4)(x-4)(x+5)
c.(x-4)(x+5)(x+5)
d.(x-4)(x+4)(x-5)

Answer 1

The +80 means there must be an even number of (x-c) terms, because the only way to get a positive result is multiplying even numbers and optionally pairs of negative numbers. We also know that it must be 4, 4, 5, not 4, 5, 5, because only the former multiplied together gives us 80. So, we can eliminate c) as a possibility because the final term would be -100, not 80. We can eliminate a) because the final term would be -80. b) and d) are both still in the running because the final term would be +80 for both.

Answer 2

Then when you do Hero's suggestion, it's easy to see which choice to take :-)

Answer 3

Okay thank you guys! Let me try it now.

Answer 4

Okay I know the common term for the first part is x^2 but I don't know how rewrite the equation. Same as the other side. Factoring isn't a strength for me , lol.

Answer 5

\[(x^3-5x^2)-(16x + 80) = x^2(x-5) - 16(x-5)\]

That can be rearranged as

\[(x-5)(x^2-16)\]

and we recognize that 16 is 4^2. \[(x-a)(x+a) = x^2-ax+ax-a^2 = x^2 -a^2\]
16 = a^2, so we can factor \[(x^2-16)\] as \[(x+4)(x-4)\] leaving us with
\[(x-5)(x-4)(x+4)\]

Answer 6

Thank you so much! @whpalmer4

Answer 7

The correct answer is d, right? @whpalmer4

Answer 8

yes, d) looks like the correct answer. If we multiply out b) we get

\[(x-4)(x-4)(x+5) = (x^2-4x-4x+16)(x+5) = \]
\[x^3+5x^2-4x^2-20x-4x^2-20x+16x+80 = x^3 - 3x^2 -24x + 80\] which is not what we started with, so b) cannot be the right answer.