Answer
(5x-3)(6x-1)
Work Step by Step
The terms of the trinomial is of the form $ax^{2}+bx+c$ whereby a=30, b = -23 and c = 3
Find two numbers where the product is $a \times c $ or $ 30 \times 3 = 90$, and their sum is equal to $b$ or -23
Factors of 90:
1 $\times$ 90, Sum = 91
2 $\times$ 45, Sum = 47
3 $\times$ 30, Sum = 33
5 $\times$ 18, Sum = 23
6 $\times$ 15, Sum = 21
9 $\times$ 10, Sum = 19
From above, we see that the only numbers that fit the above condition is 5 and 18.
As b is negative, but the product $a \times c $ is positive, both a and c have to be negative.
Thus the two numbers are -5 and -18.
Write bx as a sum of the two numbers, so -23x is written as a sum of -5x and -18x:
30$x^{2}$ -23x+3= 30$x^{2}$ -5x-18x+3
Factorize the equation by grouping:
30$x^{2}$ -5x-18x+3
= 5x(6x-1)-3(6x-1)
=(5x-3)(6x-1)
