How do you factor #3x^2-10x+7#?

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Answer 1 · 2016-06-19T09:14:30

# = color(blue)( (3x - 7 ) ( x -1) #

#3x^2 - 10x + 7#

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

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

#N_1*N_2 = a*c = 3 * 7 = 21#

AND

#N_1 +N_2 = b = -10#

After trying out a few numbers we get #N_1 = -7# and #N_2 =-3#

#(-7) * ( -3) = 21#, and # (-7) +(-3)= -10#

#3x^2 - 10x + 7 = 3x^2 color(green)(- 3x -7x) + 7#

# = 3x ( x -1) -7 ( x- 1)#

# = color(blue)( (3x - 7 ) ( x -1) #