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To factor quadratic trinomials, we find the two numbers which add to a certain number, and multiply to equal a certain number. Let me explain using the general form of a quadratic trinomial: ax2 + bx + c.
If the quadratic trinomial is monic (coefficient on x2 is 1), then you simply find two numbers which add up to the coefficient of x (b) and multiply to give the constant (c).
For example: The monic quadratic trinomial x2 - 5x + 6. Two numbers which add up to to give -5 and multiply to give 6 are -3 and -2. (-3 + -2 = -5; -3 x -2 = 6). Therefore the factors are (x - 3)(x-2).
If the quadratic trinomial is non-monic (coefficient on x2 is greater than 1), then there's a slightly different method to go around solving them. I'll show this through the example: 2x2 + 5x - 3. We start off by changing the coefficient by multiplying it by the coefficient of x2 (in this case, 2). So the new coefficient will by -6. Then we split the equation into two factors (2x )(2x ) [They are blank because we don't know the numbers yet], and divide the factors by the coefficient of x2 (which is 2). So we have (2x )(2x ) divided by 2.
Then we use the method of solving monic quadratics, and find two numbers which add to give +5, and multiply to give -6 (the new constant). In this case, the numbers are +6 and -1. (6 + -1 = 5; 6 x -1 = -6). So we put in our two numbers to get (2x + 6)(2x - 1) all over 2. Lastly, we make sure we factorise any of the factors [(2x + 6) can be factored as 2(x + 3)] to get 2(x+3)(2x-1) all over 2. And we just cancel out both twos on the numerator and denominator, and we are left with (x + 3)(2x - 1).
One last example for non-monic quadratics: 4x2 + 7x - 2. First step: Multiply coefficient of x2 with constant to get new constant (4 x -2 = -8). Then we put the coefficient of x2 over the two factors we are yet to find. So we get (4x )(4x ) divided by 4. We then find the two numbers which add to give 7 and multiply to give -8, which are +8 and -1. We then have (4x + 8)(4x - 1) all over 4. Factorise whatever we can, to get 4(x+2)(4x-1) all over 4. Cancel out the 4s and we are left with (x + 2)(4x - 1).
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What does quadratic equations using the factoring method means?
It means you are required to "solve" a quadratic equation by factorising the quadratic equation into two binomial expressions. Solving means to find the value(s) of the variable for which the expression equals zero.
Can factoring using the quadratic formula be apply to everyday life?
If you are in the mathematics field then you might be using it everyday; otherwise... not so much
In factoring a quadratic equation involving some X 's and a plain number you see that the sign in front of the X is negative and the sign in front of the plain number is positive?
That means that both of your brackets will have minus signs.
How do you convert standard form to factored form?
To convert a quadratic equation from standard form (ax^2 + bx + c) to factored form, you first need to find the roots of the equation by using the quadratic formula or factoring techniques. Once you have the roots, you can rewrite the equation as a product of linear factors, such as (x - r1)(x - r2), where r1 and r2 are the roots of the equation. This process allows you to express the quadratic equation in factored form, which can be useful for solving and graphing the equation.
Can the answer to a quadratic equation be a decimal?
Yes. You can calculate the two roots of a quadratic equation by using the quadratic formula, and because there are square roots on the quadratic formula, and if the radicand is not a perfect square, so the answer to that equation has decimal.
