How do you factor #3x^2+17x+10#?

1 Answer
Aug 10, 2015

Answer:

#color(green)((3x+2)(x+5) # is the factorised form of the expression.

Explanation:

#3x^2 +17x +10#

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*10 =30#
and,
#N_1 +N_2 = b = 17#

After trying out a few numbers we get #N_1 = 15# and #N_2 =2#
#15*2 = 30#, and #15 +2=17#

#3x^2 +color(green)(17x) +10 =3x^2 +color(green)(15x +2x) +10 #

#=3x(x+5)+2(x+5) #

#color(green)((3x+2)(x+5) # is the factorised form of the expression.