How do you factor $10x^2+29x+10$ ?

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Answer 1 · 2017-02-11T13:11:35

$(2x+5)(5x+2)$

First let's find the zeros of the polynomial by the quadratic formula:

$x=(-29+-sqrt(29^2-4*10*10))/(2*10)$

$=(-29+-sqrt441)/20$

$=(-29+-21)/20$

$x_1=(-29-21)/20=-5/2$

$x_2=(-29+21)/20=-2/5$

Since

$ax^2+by+c=a(x-x_1)(x-x_2)$ ,

you get

$10x^2+29x+10=10(x+5/2)(x+2/5)=2*(x+5/2)* 5*(x+2/5)=(2x+5)(5x+2)$

How do you factor 10x^2+29x+1010x^2+29x+10?