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# Factoring

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140
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+725

How do I factor this equation?

$$3x^2+5x+2$$

I tried, but the answer I came up with didn't match with my teacher's answers, so I want a second opinion.

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#1
+91773
+2

$$3x^2+5x+2\\$$

First you need to find two numbers that multiply to give 3*2=6

Obviously they need to be of the same sign (positive or negative)

They also need to add to 5.    Since 5 is positive both numbers must be positive.

2 and 3 work

2+3=5

2*3=6

so now you need to write 5x as 3x+2x

$$3x^2+5x+2\\ =3x^2+3x+2x+2\\ =3x^2+3x\quad+\quad2x+2\\ \text{Now factor in pairs}\\ =3x(x+1)\quad + \quad 2(x+1)\\ =(3x+2)(x+1)$$

Melody  Sep 26, 2017
#2
+725
+2

Ohhhh. Okay. I see what I did wrong. I was only thinking about adding to 5 so I tried -1 and 6. Thanks!

#3
+91773
+1

I am glad I could help.

You can expand your final answer to see if it is correct or not.

It is always good to check answers :)

Melody  Sep 26, 2017

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