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Factoring quadratics with leading coefficient greater than 1

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Factor the given quadratic equations.

3y^2+22y+24

3x^2-17x+22

5x^2+22x+8

Enclosed is an attachment with a sample of the type of explanation I'm getting, which I do not still understand after reviewing the explanation. The explanation seems very confusing.

Please provide a more complete explanation that I can easily follow step by step?

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The expert factors a quadratic with leading coefficient greater than 1.

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There are several different ways that these types of equations can be factored. The explanations that you have are generally two of the best ways to try. Another way involves dividing all three terms by the leading coefficient. This usually leaves you with fractions which may make it even harder to do. A common way to factor is to make a square and divide it into 4 separate little squares. Above and to the left of the top left square, you will put the factors of the leading term. To the left of the bottom left square and above the top right square you will put the factors of the constant term. Then you will multiply the rows and columns to fill in each square in the same way that you would fill in a ...

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