Question

Please Help I don't understand!!!! Medal!
Factor the express completely.
9r^2 + 3r - 30

Answer 1

\[9r^{2} + 3r - 30\]

Answer 2

@Loser66 @freckles @Nnesha

Answer 3

I have a few problems similar to this. I know the answer I just don't know how to solve or explain it.

Answer 4

First factor out the GCF 3

9r^2 + 3r - 30 = 3(3r^2 + r - 10)

Now we factor 3r^2 + r - 10. One way to factor 3r^2 + r - 10 quickly is to use the quadratic formula.

Use the quadratic formula to solve 3r^2 + r - 10 = 0 for r to get r = 5/3 or r = -2

You can then use those roots to construct the factorization


r = 5/3 or r = -2

3r = 5 or r = -2

3r - 5 = 0 or r + 2 = 0

(3r - 5)(r + 2) = 0


So 3r^2 + r - 10 factors to (3r - 5)(r + 2)


Therefore, 9r^2 + 3r - 30 factors to 3(3r - 5)(r + 2)

Answer 5

sorry I typed the wrong thing. wrong problem's answer.

Answer 6

Okay I understand this one thanks. Can you help me with a few more?

Answer 7

sure, 2 more

Answer 8

\[27w ^{2} - 12\]

Answer 9

and the other is \[12y ^{3} + 4y ^{2} - 9y - 3\]

Answer 10

@jim_thompson5910

Answer 11

the first one, we can factor out the GCF 3

27w^2 - 12 = 3(9w^2 - 4)

then we can factor 9w^2 - 4 further using the difference of squares rule a^2 - b^2 = (a-b)(a+b)

9w^2 - 4 = (3w)^2 - (2)^2 = (3w - 2)(3w + 2)

making 27w^2 - 12 completely factor into 3(3w - 2)(3w + 2)

Answer 12

alternatively, you can think of 9w^2 - 4 as 9w^2 + 0w - 4

and either use the quadratic formula (similar to shown above) or think to yourself "what two numbers multiply to -4*9 = -36 and also add to 0?". The answer to that question is "-6 and +6". Those two values will help you factor 9w^2 + 0w - 4 by grouping

Answer 13

making sense?

Answer 14

Yes thank you!

Answer 15

And the last one?

Answer 16

Use factor by grouping to factor


\[\Large 12y^3 + 4y^2 - 9y - 3\]

\[\Large (12y^3 + 4y^2) + (-9y - 3)\]

\[\Large 4y^2(3y + 1) + (-9y - 3)\]

\[\Large 4y^2(3y + 1) -3(3y + 1)\]

\[\Large (4y^2 -3)(3y + 1)\]

Answer 17

Thank you Thank you Thank you Thank you Thank you Thank you Thank you