Please can someone help in factorising the following quadratic using simple factors....
20x^2+7x-6
Thanks in advance.
JP
Factoring means finding (ax+ b)(cx+ d) so that the product, is equal to that. That means ac= 20, bd= -6, and ad+ bc= 7. It would be impossible to find a, b, c, and d without restricting them to integers (and might be impossible even so).
We are looking for integers a and b so that ab= 20. Well 20= 1*20, 2*10, 4*5, (-1)*(-20), (-2)*(-10), or (-4)*(-5). We are also looking for integers c and so that bd= -6. -6= (-1)*6, (-2)*3, 1*(-6), or 2*(-3). How do we decide which? TRY them! Which of those give ad+ bc= 7?
You can use the quadratic formula to factor. For , .
Factoring .
Using the quadratic formula:
.
Thus or . Now take each of these solutions:
, multiplying both sides by 5 then subtracting 2 from both sides yields:
(1) .
, multiplying both sides by 4 and adding 3 to both sides yields:
(2) .
Multiplying equations (1) and (2) together we get the factorized form of :
.