How do you factor the expression #6x^2 + 5x +1#?

Question

Genesis Allen · Accepted Answer

See a solution process below:

Because the constant is #1# we know the constant for the factored terms will also be #1#: #( 1)( 1)# Because the constant is a positive and the coefficient for the #x# term is also positive we know the signs for the constants in the factors will both be positive: #( + 1)( + 1)# Now we need to determine the factors which multiply to 6 and also add to 5 for the coefficients of the #x# terms in the factors: #1 xx 6 = 6#; #1 + 6 = 7# <- this is not the factor #2 xx 3 = 6#; #2 + 3 = 5 # <- this IS the factor #(2x + 1)(3x + 1)#

Abigail Allen · Answer

undefined To factor the expression $6x^2 + 5x + 1$, you can use the quadratic formula or factoring by grouping. However, since the expression does not easily factor, you can use the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a = 6$, $b = 5$, and $c = 1$. Plugging in these values, you can calculate the roots of the quadratic equation.