How do you factor #3y^2 -21y+36#?

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Answer 1 · 2015-08-11T16:56:05

#color(green)((3y-9)(y-4) # is the factorised form of the expression.

#3y^2−21y+36#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ay^2 + by + c#, we need to think of two numbers such that:

#N_1*N_2 = a*c = 3*36 = 108#

and,

#N_1 +N_2 = b = -21#

After trying out a few numbers we get #N_1 = -12# and #N_2 =-9#

#(-12)*(-9) = 108#, and #(-12)+(-9)= -21#

#3y^2−color(green)(21y)+36 = 3y^2color(green)(-12y-9y)+36#

#=3y(y-4) -9(y-4)#

#color(green)((3y-9)(y-4) # is the factorised form of the expression.