Solve the form ax2 - bx - c factoring polynomials ?
This tutorial will help you factor quadratics that look something like this:
2x2 -3x - 14
(Leading coefficient is not 1; the other two coefficients can be positive or negative.)
Step 1: Multiply the constant coefficient ( -14) by the leading coefficient (2). Don't forget the negative signs, if any! You get -28.
Step 2: Write down all the different ways to factor the result (which was -28) into two numbers
-28 = (-1)(+28)
-28 = (-2)(+14)
-28 = (-4)(+7)
-28 = (-7)(+4)
-28 = (-14)(+2)
-28 = (-28)(+1)
Step 3: Now, for each possible factorization, add together the two factors. You're looking for two that add up to the middle coefficient, which is -3.
-1 + 28 = 27
-2 + 14 = 12
-4 + 7 = 3
-7+4 = -3 ← found it
-14 + 2 = -4
-28 +1 = -1 Since you already found it you don't need to bother with these
Step 4. The factors you found, namely 4 and -7, add up to -3. Therefore, you can split apart the middle term, like this:
2x2 - 3x -14
= 2x2 + 4x - 7x - 14
By the way it doesn't matter in which order you put the two terms 4x and -7x.
Step 5: All your other terms are still in the correct order, right? Second degree term first, then the two first-degree terms, then the constant term. Now put parentheses around the first two and the last two terms.
(2x2 + 4x) + (-7x -14)
(If you have any negative signs, you have to be careful here. See how I've included the negative sign inside the parentheses?)
Step 6: Factor out common monomials in each of the two groups. (If you see any negative signs on the terms with variables, you should factor them out too.)
2x(x + 2) + -7(x + 2)
Step 7: If you haven't made any mistakes in the first 6 Steps, you should now see another common factor in each Term. In this example, you can see that (x + 2) is a Common factor. Factor it out using reverse distribution.
(x + 2)(2x - 7).
Step 8. Check your answer by multiplying out using FOIL.
(x + 2)(2x - 7) = 2x2 - 3x - 14 .