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1. write a quadratic equation that can be solved by factoring. solve your equation and show and explain all your work.
2. in this unit, you have learned about several different ways to solve quadratic equations. how do you determine which method to use when you’re trying to solve a quadratic equation?

They are saying to write a quadratic that can be factored so you can start with factors and then expand it like say:

(x+1)(x+2)  are arbitrary factors, then the expansion is

x^2+3x+2  which we know can then be factored to what we started with...

In general to factor a quadratic of the form ax^2+bx+c, you need to find two values, j and k, which satisfy two conditions:

ac=jk=2 and b=j+k=3, so j and k must be 1 and 2

Then you replace bx with jx and kx in the original equation to get:

x^2+x+2x+2  now factor 1st and 2nd pair of terms...

x(x+1)+2(x+1) which is equal to

(x+1)(x+2)



If j and k are integers, the above method is the quickest and easiest.

Next in line of preference is completing the square if there are fractional numbers in the original equation.

And if there are very difficult decimals or fractions it is best to just use the quadratic formula (which is derived from completing the square)