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Factor (15x^2)+14x+1
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by
WinpossibleUser3729
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Responses
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This expression can not be factored, using the greatest common factor or grouping method. So to find the factor of this expression we have to assume 15x^2 + 14x + 1 = 0
Assuming this expression
15x^2 + 14x + 1 = 0 …............ Eq 1
Roots of a given quadratic equation ax^2 + bx +c = 0
x = {-b + v (b^2 – 4ac)}/ 2a and x = {-b - v (b^2 – 4ac)}/ 2a
Using this formula finding roots of equation 1
x = {-14 + v (14^2 – 4*15*1)}/ 2*15 and x = {-14 - v (14^2 – 4*15*1)}/ 2*15
x = { -14 + v (196 – 60)}/ 30 and x = { -14 - v (196 – 60)}/ 30
x = { -14 + v(136)}/30 and x = { -14 - v(136)}/30
As these are the roots of equation 1, so equation 1 can be written as :
{x - ( -14 + v(136)/30 }{x - ( -14 - v(136)/30 }= 0
{x + 14/30 - v(136) / 30}{ x + 14/30 + v(136) / 30} =0
=> 15x^2 + 14x + 1 = {x + 14/30 - v(136) / 30}{ x + 14/30 + v(136) / 30}
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by
Winpossible
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Sep 06, 10 07:15AM PST
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More to the above answer:
Greatest common factor method:
This is very basic method in this we factor out the greatest common factor from the polynomial
Ex. 5x^3 + 10 X^2
= 5x^2(x + 2)
Grouping method:
When there is no common factor of all terms in polynomial then grouping is done to find the factor
Ex. 3ax + 6ay + 4x + 8y
= 3a(x + 2y) + 4(x + 2y)
Now this two terms have a common factor i.e. (x + 2y)
(x + 2y) (3a + 4)
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by
Winpossible
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Sep 06, 10 07:22AM PST
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