can you show me the work for factoring

Question

42a^2-43a+6

thanks

Answer 1

Because of the large coefficients it is helpful to ry to find values for a for which the polynomial os a small number. E.g. for a = 1, the value is 5.

We know that the polynomial will factor according to:

(p a + r ) (q a + s)

p*q = 42 and r*s = 6. If for a = 1 the product of the factors is 5, then it looks like we need to choose the factorization of 42 like 42 = 7*6 then we can take p = 6 and r = -1 to make the first factor 5 for a = 1.

We then take q = 7 and s = -6, so that r*s = 6. We then see that the second factor is 1 for a = 1. So the factorization becomes:

(6 a -1)(7 a - 6)