Solve in brief 3x square - x-4??

2 Answers
Zero Two
Apr 26, 2018

#(3x-4)(x+1)#

Explanation:

(This is a method my teacher developed; it gives the right answer but you should know the other ways to do it before start learning this method)

#3x^2-x-4 -> ax^2+bx+c#

Multiply the #c# by the coefficient of #x^2#

#x^2-x-12#

Then, find the factors that make -12 and add up to -1.

#(x-4)(x+3)#

Put the coefficient of #x^2# back into each bracket and simplify.

#(3x-4)(3x+3) -> (3x-4)(x+1)#

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

Jim G.
Apr 26, 2018

#x=4/3" or "x=-1#

Explanation:

#"to solve the quadratic equate to zero and factor"#

#rArr3x^2-x-4=0#

#"using the a-c method of factoring"#

#"the factors of the product "3xx-4=-12#

#"which sum to - 1 are + 3 and - 4"#

#"split the middle term using these factors"#

#3x^2+3x-4x-4=0larrcolor(blue)"factor by grouping"#

#color(red)(3x)(x+1)color(red)(-4)(x+1)=0#

#"take out the "color(blue)"common factor "(x+1)#

#rArr(x+1)(color(red)(3x-4))=0#

#"equate each factor to zero and solve for x"#

#x+1=0rArrx=-1#

#3x-4=0rArrx=4/3#

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