# algebra 2 ?

actor the quadratic expression completely.

2x^2+7x+3=_______

please show work or explain how u got it

### 7 Answers

- L. E. GantLv 74 weeks ago
It's a quadratic, so try the quadratic formula:

x = (-7 +/- sqrt(7^2 - 4*2*3))/(2*2) = (-7 +/-sqrt(49 - 24))/4 = (-7 +/- 5)/4 = -3 or -1/2so (2x+1)(x+3)or.... 2 = 2*1 and 3 = 3* 17 = 2*3 + 1*1so (2x+1)(x+3)or==> (2x^2 + x) + (6x + 3)==> x(2x+1) + 3(2x+1)==> (2x+1)(x+3)

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- Jeff AaronLv 71 month ago
Break up the middle term into two terms, i.e. find two numbers with a sum of 7 and a product of 2*3=6. So they must be 1 and 6. So we have:

= 2x^2 + x + 6x + 3

Find a common factor for the first two terms, and find a common factor for the next two terms:

= x(2x + 1) + 3(2x + 1)

Now factor using (2x + 1) as a common factor:

= (x + 3)(2x + 1)

If the above doesn't work, first find the roots using the quadratic formula:

x = (-7 +/- sqrt(7^2 - 4*2*3)) / (2*2)

x = (-7 +/- sqrt(49 - 24)) / 4

x = (-7 +/- sqrt(25)) / 4

x = (-7 +/- 5) / 4

x = (-12 or -2) / 4

x = -3 or -0.5

So the original expression must be some multiple of:

(x + 3)(x + 0.5) which is the same as x^2 + 3.5x + 1.5

We need to multiply that by 2 to get back to the original expression.

So we have 2(x + 3)(x + 0.5), which is the same as (x + 3)(2x + 1)