How do you factor the expression #5x^2+16x+3#?

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Answer 1 · 2016-04-06T12:47:10

# color(green)( (5x + 1 ) ( x + 3) # is the factorised form of the expression.

#5x^2 + 16x +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 = 5 * 3 = 15#

AND

#N_1 +N_2 = b = 16#

After trying out a few numbers we get #N_1 = 15# and #N_2 =1#

#15* 1 = 15#, and #15 + 1= 16#

#5x^2 + color(blue)( 16x) +3 = 5x^2 + color(blue)(15x + 1x) +3#

# = 5x ( x + 3) + 1 ( x + 3)#

#(x+3)# is a common factor to each of the terms

# color(green)( (5x + 1 ) ( x + 3) # is the factorised form of the expression.