Factoring by grouping help?

Question

2x^3+12x^2-5x-30
how od i factor this by grouping
please explain

Answer 1

2x^3+12x^2-5x-30

put the first two terms in one group and the last two terms in one group
(2x^3+12x^2) + (-5x-30)

factor out 2x^2 and -5
2x^2(x + 6) + -5(x + 6)

negative and position is negative
2x^2 (x + 6) - 5(x + 6)

factor out x + 6
(x + 6) (2x^2 - 5)

the second quantity is still factorable if using irrational number. But I'll just leave it like that as the answer

Answer 2

You first group 2 sections.

(2x^3+12x^2)-(5x-30)

remember when you subtract polynomials, you need to change the 'negative' sign between the grouped terms. and change the signs of the other terms to their opposite.

(2x^3+12x^2)-(5x-30) -> (2x^3+12x^2)+(-5x+30)

take out what is common from the first group. I can take out a 2x^2

Equation becomes: 2x^2(x+6) + (-5x+30)

take out what is commong from the second group. I can take out a -5. I cant take out the x in this case becasue there exists no x attached to the 30.

2x^2(x+6) + (-5x+30) -> becomes - > 2x^2(x+6) -5(x+6)

becomes the (x+6) matches to both groups, i will use it as one of my factors.


so your answer is

(2x^2 -5)(x+6)

There you go, the factoring is complete.

Answer 3

You have 2x^3 + 12x^2 - 5x - 30

Let's factor the first two terms

2x^2(x+6)

Let's factor the second two terms

-5(x+6)

so we have

2x^2(x+6) - 5 (x+6)

Factor out the GCF

(x+6) (2x^2 - 5)

And we're done

Answer 4

2x^3+12x^2-5x-30
=2x^2(x+6) -5(x+6)
=(2x^2 -5)(x+6)

Answer 5

2x²(x+6)-5(x+6)
(2x²-5)(x+6)
(√2x-√5)(√2x+√5)(x+6)