How do you factor #2x^2-5x+3#?

2 Answers
Aug 13, 2015

Answer:

#color(blue)((2x-3)(x-1)# is the factorised form of the expression.

Explanation:

#2x^2 -5x +3#

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 = 2*3 = 6#
and
#N_1 +N_2 = b = -5#

After trying out a few numbers we get #N_1 = -2# and #N_2 =-3#
#(-2)*(-3) = 6#, and #(-2)+(-3)= -5#

#2x^2color(blue)( -5x) +3 = 2x^2 color(blue)(-2x-3x) +3#

#=2x(x-1) -3(x-1)#

#color(blue)((2x-3)(x-1)# is the factorised form of the expression.

Aug 14, 2015

Answer:

factor: #y = 2x^2 - 5x + 3#

Ans: (x - 1)(2x - 3)

Explanation:

Since a + b + c = 0, use the shortcut. One factor is (x - 1) and the other is #(x - c/a) = (x - 3/2)#
Factoring form: y = (x - 1)( 2x - 3)
The shortcut avoids the lengthy factoring by grouping.