Please help me factor this by grouping? 9x to the 3power+24x to the 2power-3x-8?

Answer 1

9x^3 + 24x^2 - 3x +8
(9x^3 - 3x) + (24x^2 +8)
3x(3x^2 - 1) + 8(3x^2 +1)
(3x+ 8)(3x^2 - 1)(3x^2 +1)

Answer 2

When you are factoring by grouping, you are looking to group the order of each term by what they have in common....since the order of each of the terms doesn't matter (as long as you keep the sign in front of that term), we can change your problem to:
9x^3 - 3x +24x^2 -8. That way, 9x^3 and -3x have a 3 and an x in common, and the 24x^2 and -8 have an 8 in common. So we factor what they have in common out:
3x(3x^2 -1) + 8(3x^2-1). The whole point was to get what's in the parentheses to look the same--and they do! Then you can take 3x and +8, put them together, and put the (3x^2-1)'s together (using the distributive property backwards) and you end up with (3x+8)(3x^2-1). Your original algebraic expression has been factored!

Answer 3

ok buddy, here it goes:
so your question is: 9x^3 + 24x^2 - 3x - 8 (Note: ^ means to the power of)

now what u do first of all, is look at the coefficients ( the number infront of the x's and the constant value, which is 8)

so u can easily tell that 9x^3 and 3x both can be divisible by 3
u can aslo tell that 24x^2 and 8 are divisible by 8

so what u do now is put those two groups side by side, and you get:
9x^3 - 3x + 24x^2 - 8
you factor them accordingly:
3x(3x^2 - 1) + 8(3x^2 - 1)
now you're pretty much done, jus put them together, making it:
(3x + 8) (3x^2 - 1) <---- that's the answer

the best way to know that you've factored correctly is that the terms inside the brackets are exactly the same. then you take the numbers outside the brackets and make them into a term. and you use the constant terms (the ones inside the brackets) and put them down as another term
and there you go
you're two terms

Answer 4

9x^3 + 24x^2 - 3x - 8
(9x^3 + 24x^2) + (-3x - 8)
3x^2(3x + 8) - (3x + 8)
(3x^2 - 1)(3x + 8)

Answer 5

(3x^2 - 1)(3x + 8)