Answer:
Part A
The factored form of the expression, 6·x² - 13·x + 6 is (2·x - 3) × (3·x - 2)
Part B
The solution of the equation 6·x² - 13·x + 6 = 0 are x = 3/2 or x = 2/3
Explanation:
Part A
The given expression to factorize is 6·x² - 13·x + 6, which can be written as follows;
6·x² - 13·x + 6 = 6·x² - 4·x - 9·x + 6
The 13·x is split at - 4·x - 9·x
6·x² - 4·x - 9·x + 6
2·x·(3·x -2) - 3·(3·x - 2)
Bringing out the common factor (3·x - 2) gives;
(2·x - 3) × (3·x - 2)
Therefore, the expression 6·x² - 13·x + 6 in factored form is (2·x - 3) × (3·x - 2)
Part B
Solving the equation, 6·x² - 13·x + 6 = 0, therefore gives;
6·x² - 13·x + 6 = (2·x - 3) × (3·x - 2) = 0
Therefore, either (2·x - 3) = 0 and x = 3/2 or (3·x - 2) = 0 and x = 2/3
From which we have 6·x² - 13·x + 6 = 0 when x = 3/2 or 2/3 and x = 3/2 or x = 2/3 are the solution of the equation 6·x² - 13·x + 6 = 0.