Intermediate Algebra Factoring

[Poker-face]

Does anybody know any tips on factoring large numbers.

For example- x[2] - 70x + 901=0

I keep running into large numbers like these and spend a lot of time trying factor them out. Is their any short cut other than just trial and error?

Thanks, EG

 

[Mark44]

Does anybody know any tips on factoring large numbers.

For example- x[2] - 70x + 901=0

I keep running into large numbers like these and spend a lot of time trying factor them out. Is their any short cut other than just trial and error?

Thanks, EG

Start by factoring 901. You want two factors that multiply to make 901 and that add to make -70.

 

[Poker-face]

I understand that, but how do you know which numbers equal 901 without randomly picking numbers, or is it truly trial and error?

 

[Mark44]

No, it's not a random process at all, and it isn't trial and error, either.
901 is odd, so you don't need to try 2, 4, 6, 8, and so on.
901 isn't a multiple of 3 (the digits don't add up to 3), so you don't need to try 3, 6, 9, 12, ...
901 doesn't end in a 0 or 5, so you don't need to try 5, 10, 15, 20, ...

All you need to do is check prime numbers up to 30, which is approximately the square root of 901. If you go past 30, the other factor will be less than 30, so you should already have caught it

 

[Poker-face]

Their are also asking me to find the square root of numbers like 1/117,649. how do you break this numbers without a calculator?

Thanks, EG

 

[Poker-face]

No, it's not a random process at all, and it isn't trial and error, either.
901 is odd, so you don't need to try 2, 4, 6, 8, and so on.
901 isn't a multiple of 3 (the digits don't add up to 3), so you don't need to try 3, 6, 9, 12, ...
901 doesn't end in a 0 or 5, so you don't need to try 5, 10, 15, 20, ...

All you need to do is check prime numbers up to 30, which is approximately the square root of 901. If you go past 30, the other factor will be less than 30, so you should already have caught it

I see, what do you mean bye (the digits don't add up to 3)?

 

[Mark44]

Their are also asking me to find the square root of numbers like 1/117,649. how do you break this numbers without a calculator?

Thanks, EG

Let's just look at the denominator - 117,649

100 * 100 = 10,000
300 * 300 = 90,000
400 * 400 = 160, 000
so for the square root of 117,649, you're looking for a number between 300 and 400, but closer to 300 than 400. The last digit of 117,649 is 9, so the last digit of its square root has to be 3. So try 303 (probably too small), 313, 323, and so on. Whatever answer you get, take the reciprocal for the square root of 1/117,649.

 

[Poker-face]

Let's just look at the denominator - 117,649

100 * 100 = 10,000
300 * 300 = 90,000
400 * 400 = 160, 000
so for the square root of 117,649, you're looking for a number between 300 and 400, but closer to 300 than 400. The last digit of 117,649 is 9, so the last digit of its square root has to be 3. So try 303 (probably too small), 313, 323, and so on. Whatever answer you get, take the reciprocal for the square root of 1/117,649.

Thanks that clarifies that>

 

[Mark44]

I see, what do you mean bye (the digits don't add up to 3)?

For any number that's divisible by 3, the digits add up to 3 or a multiple of 3.

18 --> 1 + 8 = 9
48 --> 4 + 8 = 12

If the digits don't add up to 3 or a multiple of 3, the number is not divisible by 3. For example, 1,000,007 is not divisible by 3, since the digits add up to 1 + 7 = 8.

There's a similar rule for 9. For any number that is divisible by 9, the digits add up to a number that is divisible by 9.

243 --> 2 + 4 + 3 = 9
243 = 9*27

1,000,026 --> 1 + 2 + 6 = 9
1,000,026 = 9 * 111,114

 

[Poker-face]

Awesome, thanks for the quick response.