Question 160318
How do you factor completely: {{{3x^2 + 17x + 10}}}? Whats the answer?
<pre><font size = 4 color = "indigo"><b>
{{{3x^2 + 17x + 10}}}

Multiply the 3, (coefficient of {{{x^2}}} by the 10, 
(constant term), getting 30.

Write all the pairs of integers that have product 30

{{{matrix(4,1,1*30,2*15,3*10,5*6)}}}

Beside them write their sums:

{{{matrix(4,2,1*30,1+30=31,2*15,2+15=17,3*10,3+10=13,5*6,5+6=11)}}}

Pick out the one that has the sum 17, the coefficient of {{{x}}}.

{{{matrix(1,2,2*15,2+15=17)}}}

Rewrite the 17 in

{{{3x^2 + 17x + 10}}}

as {{{(2+15)}}}

{{{3x^2 + (2+15)x + 10}}}

Distribute and rewrite {{{(2+15)x}}} as {{{2x+15x}}}

{{{3x^2 + 2x+15x + 10}}}

Factor {{{x}}} out of the first two terms:

{{{x(3x + 2)+15x + 10}}}

Factor {{{5}}} out of the last two terms:

{{{x(3x + 2)+5(3x + 2)}}} 

Foctor {{{(3x+2)}}} out of each:

{{{(3x + 2)(x+5)}}}

Edwin</pre>