![]() ![]() Well, factoring the quadratic equation then sets us up to be able to find out where exactly our roots are, and our roots just mean where our graph is equal to zero. Well, if you recall a quadratic equation is always a parabola (or U-shaped graph). ![]() Maybe you’re asking, why on earth do I even need to factor? Why can’t I just leave it as it is? \(x^2\) and \(x\) share a common factor of \(x\). But, we still have something that can be factored out. Now, we have \(8(x^2 + 2x)\) being multiplied by everything on the inside. So, we can go ahead and factor out that 8. ![]() Well, 8 and 16 share a common factor of 8. What are the common factors of \(8x^2 + 16x = 0\)? Say we have the equation \(8x^2 + 16x = 0\) The easiest way to do this is to find the common factor. Now, expanding can be pretty easy we know exactly what to do to expand them when given our factors, but figuring out how to factor our expanded version can be a little harder. So, again we have our factors \((x + 2)(x + 6)\) on the left, and when you multiply that you get the expanded version: \((x^2+ 8x + 12)\). Once you multiply together you get \(x^2+ 8x + 12\). The actual quadratic equation is the expanded, or multiplied out version, of your two factors that are being multiplied.įor example, \((x + 2)\) and \((x + 6)\) are my factors that are being multiplied together. Now we have to divide the two factors +6 and +9 by the coefficient of x 2, that is 2.In order to factor a quadratic, you just need to find what you would multiply by in order to get the quadratic. So, m ultiply the coefficient of x 2 and the constant term "+27".ĭecompose +54 into two factors such that the product of two factors is equal to +54 and the addition of two factors is equal to the coefficient of x, that is +15. In the given quadratic equation, the coefficient of x 2 is not 1. In the given quadratic equation, the coefficient of x 2 is 1.ĭecompose the constant term +14 into two factors such that the product of the two factors is equal to +14 and the addition of two factors is equal to the coefficient of x, that is +9.įactor the given quadratic equation using +2 and +7 and solve for x.ĭecompose the constant term +14 into two factors such that the product of the two factors is equal to +14 and the addition of two factors is equal to the coefficient of x, that is -9.įactor the given quadratic equation using -2 and -7 and solve for x.ĭecompose the constant term -15 into two factors such that the product of the two factors is equal to -15 and the addition of two factors is equal to the coefficient of x, that is +2.įactor the given quadratic equation using +5 and -3 and solve for x.ĭecompose the constant term -15 into two factors such that the product of the two factors is equal to -15 and the addition of two factors is equal to the coefficient of x, that is -2.įactor the given quadratic equation using +3 and -5 and solve for x. (iv) Write the remaining number along with x (This is explained in the following example). (iii) Divide the two factors by the coefficient of x 2 and simplify as much as possible. (ii) The product of the two factors must be equal to "ac" and the addition of two factors must be equal to the coefficient of x, that is "b". ![]() (i) In a quadratic equation in the form ax 2 + bx + c = 0, if the leading coefficient is not 1, we have to multiply the coefficient of x 2 and the constant term. Solving Quadratic Equations by Factoring when Leading Coefficient is not 1 - Procedure Positive sign for smaller factor and negative sign for larger factor. ![]()
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