How do you factor #40-5t^3#?

1 Answer
Jun 7, 2018

Answer:

#5(8-t^3)#

Explanation:

BACKGROUND: FACTORING IN GENERAL
To factor you have to find the Greatest Common Factor, just like if someone told you,

"Factor 3+6+9x"

Since only 9 has an x attached to it and the others don't, do not even consider factoring out an x. And luckily in this example, there are no other variables. So now we just look at the numbers: 3, 6, 9.

And to solve this question we simply have to ask ourselves one other question: "What is the GCF of 3, 6, and 9?"
And the answer to that is 3.
So we factor out a 3.
And when we do this, it is kind of like separately dividing each term by 3, which gives us our answer:

#3(1+2+3x)#

BACKGROUND: FACTORING WITH (COMMON) VARIABLES
In general, when factoring expressions with variables, you always take the smallest exponent.
Example:

#3x+6x^2+9x^3#

So we can see that we factor out a 3 right off the bat, but now, what about the variables???

Like I said, when factoring, it's kind of like separately dividing each term by the GCF(aka thing they all have in common :P)

Because of this, we can't possibly factor out a number larger. That's like dividing 3 by 14. Which isn't possible if you want non decimal numbers, since 14 is larger than 3.

So when factoring the variable part out, we have to take the one with the smallest exponent, in this case #x^1# or just #x#.

Then your answer would be:

#3x(1+2x+3x^2)#

ON TO YOUR QUESTION:
All we do is look at the coefficients: 5 and 40.
Since 40 is divisible by 5, the GCF is 5.

Factoring, we get:

#5(8-t^3)#

That is your answer.

Note: I truly apologize for how long this was! But I hope this helps for this question, and for the future.