8x^2+59x+21

I did this in my head and on my phone that is why i did not explain myself.  I shall try to do so now.

 

8x^2+59x+21 can it be factor?

 

I looked for 2 numbers that was with a product of 8*21    And a sum of  59

8+21=29 the sum is too little.  the factors will need to be further apart.

4+42=58 Mmm close but not right.

Now I notice that 21=3*7 so I will try 3 and 7*8  That is 3 AND 56

that works!  3*56=3*7*8=8*21  and  3+56=59

now I did this in my head.  You do not need to do all the multiplications just think about the factors.

Anyway now

$$\begin{array}{rll}
8x^2+59x+21&=&8x^2+56x+3x+21\\
&=&8x(x+7)+3(x+7)\\
&=&(8x+3)(x+7)
\end{array}$$

Split 59x into 56x+3x

then factorise in pairs

that'll work :))