SOLUTION: Can you please help me I need help with factor by grouping... 3x^3 + 15x^2 - 12x^2 - 60x How can you group them when they all have different exponents????

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you please help me I need help with factor by grouping... 3x^3 + 15x^2 - 12x^2 - 60x How can you group them when they all have different exponents????       Log On


   

Question 164790: Can you please help me
I need help with factor by grouping...
3x^3 + 15x^2 - 12x^2 - 60x
How can you group them when they all have different exponents????
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please help me
I need help with factor by grouping...
3x^3 + 15x^2 - 12x^2 - 60x
How can you group them when they all have different exponents????
-------------------------
You can't, only terms with the same exponent can be grouped. The 2 middle terms are x^2, so add those.
3x%5E3+%2B+3x%5E2+-+60x
Then divide by 3x, the largest common factor
= 3x%2A%28x%5E2+%2B+x+-+20%29
Then factor the trinomial.
= 3x%2A%28x%2B5%29%2A%28x-4%29

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
3x^3 + 15x^2 - 12x^2 - 60x
(3x^3 + 15x^2) - (12x^2 + 60x)
Notice the sign change in the second group.
.
Now, factor each group:
3x^2(x + 5) - 12x(x + 5)
.
Now, factor out (x+5)
(x+5)[3x^2 - 12x]
.
Now, factor terms inside the []:
(x+5)(3x)[x - 4]
Resulting in:
(3x)(x+5)(x-4)