How do you factor $10 x^{2} + 11 x + 3$ $10x^2 + 11x + 3$ ?

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How do you factor $10 x^{2} + 11 x + 3$ $10x^2 + 11x + 3$ ?

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Answer 1 · 2015-05-17T08:19:46

$10 x^{2} + 11 x + 3$ $10x^2+11x+3$ is of the form $a x^{2} + b x + c$ $ax^2+bx+c$ with $a = 10$ $a=10$ , $b = 11$ $b=11$ and $c = 3$ $c=3$ , so we can calculate the discriminant as follows:

$Delta = b^2-4ac = 11^2 - (4xx10xx3) = 121 - 120 = 1 = 1^2$

...a positive perfect square. So $10x^2+11x+3$ has two distinct rational roots, given by the formula:

$x = (-b+-sqrt(Delta))/(2a) = (-11+-1)/20$

That is $x = -12/20 = -3/5$ and $x = -10/20 = -1/2$

Since $x = -3/5$ is a root, $(5x+3)$ must be a factor.

Since $x = -1/2$ is a root, $(2x+1)$ is the other factor.

So $10x^2+11x+3 = (5x+3)(2x+1)$

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How do you factor $10 x^{2} + 11 x + 3$ $10x^2 + 11x + 3$ ?

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