How do you factor #3x^2 − x − 4#?

Question

Savannah Anderson · Accepted Answer

#3x^2-x-4=(x+1)(3x-4)# To factorize #3x^2-x-4# first multiply coefficient of #x^2# and constant term. As they are #3# and #-4# respectively, their product is #-12# Now split #-12# in two parts whose sum is equal to coefficient of #x# i.e. #-1#. Here they will be #-4# and #3# Hence #3x^2-x-4# = #3x^2-4x+3x-4# = #x(3x-4)+1(3x-4)# = #(x+1)(3x-4)#

Eli Assouline · Answer

#(x+1)(3x-4)# #"factor using the a-c method"# #"the factors of the product "3xx-4=-12# #"which sum to - 1 are + 3 and - 4"# #"split the middle term using these factors"# #rArr3x^2+3x-4x-4larrcolor(blue)"factor in groups"# #rArrcolor(red)(3x)(x+1)color(red)(-4)(x+1)# #"take out the common factor "(x+1)# #=(x+1)(color(red)(3x-4))# #rArr3x^2-x-4=(x+1)(3x-4)#

Ethan Adkins · Answer

undefined To factor the quadratic expression 3x^2 − x − 4, you can use the factoring by grouping method or the quadratic formula. Since the expression cannot be factored easily using the grouping method, you can use the quadratic formula, which is x = [-b ± √(b^2 - 4ac)] / (2a). By substituting the coefficients a = 3, b = -1, and c = -4 into the quadratic formula, you can solve for the roots of the quadratic equation.