Question 1172888
<br>
Two other tutors have shown methods for factoring quadratics like this one using different purely algebraic methods.<br>
Both methods are good; and there are many other similar methods.  But I prefer the basic method that -- at least when I was learning algebra 60 years ago -- was always used.<br>
We want to factor the expression as<br>
{{{25x^2+30x+8 = (ax+b)(cx+d)}}}<br>
where a, b, c, and d are integers.<br>
The positive constant term 8 tells us the constants b and d are the same sign; then the positive linear term 30x tells us b and d are both positive.<br>
a and c have to multiply to 25; and b and d have to multiply to 8.  There are not many possibilities:
a and c are 25 and 1, or 5 and 5
b and d are 1 and 8, or 2 and 4, or 4 and 2, or 8 and 1<br>
Try different combinations until you find the one that gives the correct middle term, 30x.<br>
Fast and easy calculations show the answer to be<br>
{{{25x^2+30x+8 = (5x+4)(5x+2)}}}<br>