Question 1099933
First step - take out common factors:
{{{10x^5+11x^4+3x^3=x^3(10x^2+11x+3)}}}
 
Now you have to factor {{{10x^2+11x+3}}} .
I assume you were told that you could split the middle term into two terms,
and then "factor by grouping",
finding the coefficients of the split terms as factors of {{{ac}}} ,
where {{{a}}}  is the coefficient of {{{x^2}}} and {{{c}}} is the independent term.
{{{a=10}}} and {{{c=3}}} , so {{{ac=10*3=30}}} .
You want to find a pair of numbers (factors of 30)
whose product is {{{30}}} , and whose sum is {{{11}}} .
Because the product and the sum are positive,
you know that the two factors are positive.
Nice, we do not have to worry about negative numbers.
The pairs of numbers that give {{{30}}} as a product are
{{{1*30=30}}} ,
{{{2*15=30}}} ,
{{{3*10=30}}} , and
{{{5*6=30}}} .
So, we pick {{{5}}} and {{{6}}} ,
because they add to the middle term: {{{5+6=11}}} .
Writing only the part to be factored,
{{{10x^2+11x+3=10x^2+5x+6x+3=5x(2x+1)×3(2x+1)=(5x+3)(2x+1)}}} .
So, after all that work,
{{{10x^5+11x^4+3x^3=highlight(x^3(5x+3)(2x+1))}}} .