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

2 Answers
Aug 10, 2018

Answer:

#3x^2-17x+10=(3x-2)(x-5)#

Explanation:

In the quadratic polynomial #3x^2-17x+10#, the coefficient of #x^2# and constant term are of same sign and their product is #30#,

hence we should split #-17#, the coefficient of #x#. in two parts, whose sum is #17# and product is #30#. These are #2# and#15# and hence

#3x^2-17x+10#

= #3x^2-15x-2x+10#

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

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

Note - If sign of coefficient of #x^2# and constant term are different, find two numbers whose difference is equal to the coefficient of #x#.

Aug 10, 2018

Answer:

#(x-5)(3x-2)#

Explanation:

#"factor the quadratic using the a-c method"#

#"the factors of the product "3xx10=30#

#"which sum to "-17" are "-15" and "-2#

#"split the middle term using these factors"#

#3x^2-15x-2x+10larrcolor(blue)"factor by grouping"#

#=color(red)(3x)(x-5)color(red)(-2)(x-5)#

#"take out the "color(blue)"common factor "(x-5)#

#=(x-5)(color(red)(3x-2))#

#3x^2-17x+10=(x-5)(3x-2)#