Working these out?

[chadsobey]

I'm having trouble on a math packet that's due tomorrow. I did some of the problems and I'll tell you the answer I got, I'm not sure if they're wrong or right. Would you mind working these out and telling me what I did wrong if I did? Thanks so much.

1. (2x+1)(x+3)=0
The answer I got for this one was (-1/2, -3)

2. (3x-1)(x+4)=0
I got (1/3, -4) as my answer.

3. (3x-1)(x-3)=0
I got (1/3, 3)

4. (2x+5)(x+5)=0
My answer was (-5/2, -5)


Also, I need help on these four. I didn't get an answer for these because I didn't know how to (please bare with me! haha)

8. y=5x^2+8x-4

9. y=5x^2+22x-15

10.y=3x^2+x-2

11. y=3x^2-11x+6


If you can explain any of these it would be GREAT. thanks!

 

[galactus]

8. y=5x^2+8x-4

The first 4 look good. I will spell this one out so you can do the others. Okey-doke?.

Since the coefficients of x^2 is not 1, but 5, we multiply that by the constant and get -20.

Now, ask what two numbers when multiplied equal -20 and when added equal 8 (the coefficient of x)?.

How about 10 and -2?.

\(\displaystyle 5x^{2}+\underbrace{10x-2x}_{\text{8x}}-4\)

Group:

\(\displaystyle (5x^{2}+10x)-(2x+4)\)

Factor a common term out of each group:

\(\displaystyle 5x(x+2)-2(x+2)\)

Inside the parenthese is the same. That is imperative.

Factor out the x+2 and write as \(\displaystyle (5x-2)(x+2)\)

That's it.