See the screenshot below
I've filled out the empty boxes with the proper numbers and/or algebraic expressions.
Your teacher is using the AC method, sometimes called the diamond method. The first coefficient 3 is multiplied with the last term 10 to get 30. This is placed up top as shown in that diagram.
The 11 down below should be a -11. Your teacher made a typo.
We're tasked to find two numbers that...
- multiply to 30
- add to -11
Through trial and error, or basically using what your teacher gave you, you should find that the two numbers are -6 and -5
- -6 times -5 = 30
- -6 plus -5 = -11
It appears the factors are 3x-6 and 3x-5.
Notice that 3x times 3x = 9x^2, but we want 3x^2 instead. What we can do is divide each piece of 3x-6 by 3 to end up with x-2
That way we have 3x times x = 3x^2 like we want.
So we have (x-2) and (3x-5) as the two factors
Check out the diagram below to see how I've placed them along the edges of the table. The diagram also shows how the rest of the table is filled out.
Let's finish up and solve for x
3x^2 - 11x + 10 = 0
(x-2)(3x-5) = 0
x-2 = 0 or 3x-5 = 0 ..... zero product property
x = 2 or 3x = 5
x = 2 or x = 5/3 ... are the two solutions
I've marked these solutions in the screenshot below.