Question

factor: 6x^2+5x+1

Answer 1

(3*x+1)*(2*x+1)

Answer 2

@confusedengineer : Thank you for contributing. However, I ask that you please follow the OpenStudy Code of Conduct, which asks that no helper provide direct answers without the involvement of the questioner. On the other hand, if you could guide kekenicole towards finding the factors, so that she can find them herself, that'd be great. Thank you.

Answer 3

@kekenicole

I'll do an example with a different polynomial: \[6x^2-2x-20\]

The method I use to factor polynomials like this where the leading term has a coefficient other than 1 is as follows:

Multiply the coefficients of the first and last terms: 6*-20 = -120
Now find a pair of factors of that product which sum to the coefficient of the middle term:
-12,10 is such a pair, as -12*10 = -120 and -12+10 = -2

Now rewrite the polynomial, splitting the middle term with the two coefficients just found:
\[6x^2-12x+10x-20\]Group pairs of terms:\[(6x^2-12x)+(10x-20)\]Factor each group:\[6x(x-2)+10(x-2)\]Notice there is a common factor to each product term. Factor it out:\[(x-2)(6x+10)\]

Check the work by multiplication:
\[(x-2)(6x+10) = x(6x+10)-2(6x+10) = 6x^2+10x -12x -20\]\[\qquad=6x^2-2x-20\checkmark\]