How would I factor equations like this? x^2 + 3x + 2. or x^2 - 2x - 15thank you

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neela | High School Teacher | (Level 3) Valedictorian

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There are two  quadratic expressions given.

x^2+3x+2 and  x^2-2x-15. To find the factors.


To find the factors of x^2+3x+2, we split the middle term 3x  into two terms in sich a way that the  product of the two split terms equal to the first and last term.

3x  is split into two terems 2x + x. Product of the split terms = 2x*x = 2x^2. Product of the 1st and last terms = x^2 * 2 = 2x^2.

Now group the terms and find the common factors (CF) for each group.


x(x+2) +1(x+2). x+2 is the CF.

Take out the CF:




-2x = (-5x)+(3x). And (-5x)*(3x) = x^2*(-15).

Therefore x^2-2x-15 = (x^2 -5x)+(3x-15) = x(x-5)+3(x-5) = (x-5)(x+3).

x^2-2x-15 = (x-5)(x+1).