Question

factor
10x^3(x-4)-5x(x-4)

Answer 1

\[a^b(u^t) = au^{b+t}\]

Answer 2

that is no help thanks for trying

Answer 3

@abb0t Doesn't it have to be the case that \(a=u\)?

Answer 4

ok :(

Answer 5

i do not mean to sound ungrateful abbot but using those formulas confuses me if you want to teach me then using a similar problem works better

Answer 6

Try dividing both terms by \(5x\) to factor it out.

Answer 7

2x^3(x-4)-(x-4) sound right

Answer 8

Similar Problem:

7x(x-5) - 2(x-5)

factors to

(7x - 2)(x - 5)

because you can factor out the GCF x-5

Answer 9

jim thanks for the similar problem its starting to make more sense
10x^3(x-4)-5x(x-4)
(10x^3-5x)(x-4)

Answer 10

yep now factor 10x^3-5x

Answer 11

you can factor that piece down further

Answer 12

5x^2

Answer 13

gcf of 10 and 5 is ____

Answer 14

five goes in to ten and its self so the gcf is five

Answer 15

the gcf of x^3 and x is ___

Answer 16

x^3

Answer 17

replace x with a number if you have to

say x = 9

x^3 = 9^3

x = 9

gcf of x^3 and x

is the same as saying

gcf of 9^3 and 9

Answer 18

\[10x^3(x-4)-5x(x-4)\]
\[5x(x-4)[2x^2-1]\]

Answer 19

Just take out the 5x(x-4).

Answer 20

thanks azteck but jim was showing me how to get to that all you did is confuse me

Answer 21

were you able to figure out the GCF of x^3 and x ?

Answer 22

no

Answer 23

how about the gcf of 9^3 and 9?

Answer 24

9 the gcf is three so 9^3 would be 3^3 right

Answer 25

@vortish You shouldn't be doing factorising exercises if you haven't completely understood the concept of HCF (Highest Common Factor)

Answer 26

9^3 = 9*9*9

so

the GCF of 9^3 and 9

is the same as saying

the GCF of 9*9*9 and 9

Answer 27

9*9*9 and 9 have one single '9' in common and this is the largest common factor

so the GCF of 9^3 and 9 is 9

Answer 28

azteck pls leave all you are doing is ticking me off

Answer 29

that make sense Jim sense 9 does go into it self by one

Answer 30

the GCF of 7^3 and 7 is 7

the GCF of 8^3 and 8 is 8

etc etc

this works for any number, so in general, you can say

the GCF of x^3 and x is x

Answer 31

right

Answer 32

put this together:

the GCF of 10 and 5 is 5
the GCF of x^3 and x is x

turns into

the GCF of 10x^3 and -5x is 5x

so you can factor out the GCF to go from

10x^3 - 5x

to

5x(2x^2 - 1)

Answer 33

notice how if you distribute that 5x back in, you'll get 10x^3 - 5x again

Answer 34

Im sorry Jim and Abbot for my out burst but Azteck was not teaching me the correct way to get to the solution and im a 36 year old man trying to figure out algebra after twenty years of being out of school im trying to make a better life for my kids and he was just making it harder

Answer 35

ok Jim that makes sense

Answer 36

so you can see that

10x^3(x-4)-5x(x-4)

becomes

(10x^3-5x)(x-4)

which further completely factors to

5x(2x^2-1)(x-4)

Answer 37

right thanks for the help Jim and Abbot thank you for you effort in explaining this problem to me