How do you factor #4x^{2}-3x-1#?

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Answer 1 · 2016-10-06T17:52:25

#4x^2-3x-1=(x-1)(4x+1)#

#4x^2-3x-1=(x-1)(4x+1)#

Answer 2 · 2016-10-06T17:52:38

Factorising is the reverse of multiplying brackets.

multiply the a and c terms

#4 xx (-1)=-4#

find factors of# -4 # that add to the b term, in this case #-3 #

replace the b term with these two factors as coefficients

so the quadratic becomes

#4x^2-4x+x-1#

group the terms into pairs and factorise by grouping

#(4x^2-4x)+(x-1)#

#4x(x-1)+(x-1)#

#(4x+1)(x-1)#

If you work from the bottom of the page upwards you see the method is the reverse of multiplying out the brackets.