How do you factor the trinomial #10x^2 + 11x + 3#?

2 Answers
Jul 17, 2017

#(2x+1)(5x+3)#

Explanation:

#"'split the x-term and factorise by grouping"#

#10x^2+5x+6x+3larr (5x+6x=11x)#

#color(red)(5x)(2x+1)color(red)(+3)(2x+1)#

#"factor out "(2x+1)#

#(2x+1)(color(red)(5x+3))#

#rArr10x^2+11x+3=(2x+1)(5x+3)#

Jul 17, 2017

#(5x+3)(2x+1)#

Explanation:

#10x^2 +11x+3#

Find factors of #10 and 3# whose products ADD up to #11#

#3# is a prime number, so there are not very many options to try.
Using #10# will not work - the sum will be too big, try #2 and 5#
Cross multiply the factors and add the products till you get #11#.

#" "10 and 3#
#" "darr" "darr#

#" "5color(white)(xxxx)3" "rarr 2xx3 = 6#
#" "2color(white)(xxxx)1" "rarr 5xx1 = ul5#
#color(white)(xxxxxxxxxxxxxxxx.xx)11#

The signs are both positive.

#(5x+3)(2x+1)#

There are clues in the original expression.

#10x^2 +11xcolor(blue)(+)3#

#color(blue)(+)# sign tells you 2 things:
#rarr# ADD the products of factors of #10 and 3#
#rarr# the SIGNS will be the SAME.

The (+) sign of the 'b' which is #+11# tells you they will be positive.