What is the largest integer number a for which a³ + 25 is divisible by a + 5?

[Pedrzi]

I've been trying to do this one for 2 hours already:

What is the largest integer [imath]a[/imath] for which [imath]a^3 + 25[/imath] is divisible by [imath]a + 5[/imath]?

i've no idea of what to do

 

[stapel]

I've been trying to do this one for 2 hours already:

What is the largest integer [imath]a[/imath] for which [imath]a^3 + 25[/imath] is divisible by [imath]a + 5[/imath]?

i've no idea of what to do

You know that [imath]a^3 + 25[/imath] is a sum of cubes. You know that a sum of cubes will factor. After you applied the factorization formula and did the indicated division, what was your result and what were your thoughts?

Please be complete. Thank you!

Eliz.

 

[Dr.Peterson]

You know that \(a^3 + 25\) is a sum of cubes.

Unfortunately, it's 25, not 27.

But [imath]a^3 + 125[/imath] has [imath]a + 5[/imath] as a factor. Try using that, by writing [imath]a^3 + 25[/imath] as [imath]a^3 + 125 - 100[/imath] and doing the division.

 

[khansaheb]

I've been trying to do this one for 2 hours already:

What is the largest integer [imath]a[/imath] for which [imath]a^3 + 25[/imath] is divisible by [imath]a + 5[/imath]?

i've no idea of what to do

Have you tried polynomial division ?

What is the remainder of that division?

 

[stapel]

Unfortunately, it's 25, not 27.

D'oh! I certainly mis-read that! Thank you for the correction!

Eliz.

 

[Steven G]

D'oh! I certainly mis-read that! Thank you for the correction!

Eliz.

Just to let you know, we still have corner time.

 

[stapel]

Just to let you know, we still have corner time.

Do I get to wear the pointy hat? ?

 

[Steven G]

Do I get to wear the pointy hat? ?

Sure. Just to remind you that it's always 90 degrees in the corner.