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algebra 2 ?
actor the quadratic expression completely.
2x^2+7x+3=_______
please show work or explain how u got it
8 Answers
- 3 months ago
2 (x2 + 7x + 3)
= 4x2 + 14x + 6
= 4x2 + 14x + 6 - 6 = 0 - 6
= 4x2 + 14x = (-6)
= 4x2 + 14x = - 6
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2
Final result would be:
2x2 + 7x = -6
- L. E. GantLv 77 months 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)
- Jeff AaronLv 78 months 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)