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You put the quadratic equation in the form polynomial = 0, and then factor the polynomial. A product is zero if one of its factors is zero. Example:
x2 - 5x + 6 = 0
(x-3)(x-2) = 0
x-3 = 0 or x-2 = 0
x = 3 or x = 2
This is a special case of quadratic equations when a is 1. In the above example, c (6) is a small number, then factoring looks simple. However, when c is a big number and contains itself many factors, then factoring becomes complicated and consumes lot of time.
Example 1. Solve: x^2 + 34x - 72 = 0
Example 2. Solve: -x^2 - 26x + 56 = 0
In these cases, the trial and error process to find the correct terms of the two binomials consumes too much time.
There is a new method, called Diagonal Sum Method, that can quickly and directly give the 2 real roots, in these examples, WITHOUT FACTORING.
See Discussion for details.
One of the main reasons this is done is to solve quadratic equations. If you have an equation such as:
x squared + 5x + 6 = 0
(and it is important in this case that the right side be equal to zero), you can solve this through factoring as follows:
(x + 3) (x + 2) = 0
The product can only be equal to zero if one of the factors is zero, so either:
x + 3 = 0
or:
x + 2 = 0
If you solve the two equations separately (which is easy, in this factored form), you get the two solutions (-3, and -2). You can easily check that these are, indeed, solutions to the original equation. Just replace and do the calculations.
Find the expressions which when multiplied give the equation.
eg x2 + 5x + 6 = (x + 2)(x + 3)
Add your answer:
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What two basic approaches are used to factor expressions?
Look for recognizable patterns based on types of expressions. or guess and check.
How do you factor this quadratic x2-3x 2?
(x - 2)(x - 1)
What is the greatest common factor of the two algebraic expressions 16r3 28r?
The GCF is 4r.
15Y2 plus 26y plus 8 greatest common factor?
using the quadratic formula -4/3 and -0.4
What is the GCF ofz3-3z2?
The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers or expressions. You have only one expression in the question! The greatest factor of any number is itself.
Can all quadratic expressions be factorised?
Only when the discriminant of the quadratic expression is equal to or greater than zero
What do you do with remainders in quadratic expressions?
Leave it the way it is. (by Stephen Hawking)
Does quadratic equation relate to science?
No, the quadratic equation, is mainly used in math to find solutions to quadratic expressions. It is not related to science in any way.
Is the foil method used for factoring quadratic equations?
Yes FOIL method can be used with quadratic expressions and equations
What is the quadratic equation used for?
It is used to solve quadratic equations that cannot be factored. Usually you would factor a quadratic equation, identify the critical values and solve, but when you cannot factor you utilize the quadratic equation.
How do you factor of a4 plus b4-7a2b2?
Usually simple substitutions enable such expressions to be seen as quadratic expressions. The substitutions x = a2 and y = b2 give a4 + b4 - 7a2b2 = x2 - 7xy + y2 which does not have any rational factors. Consequently, the quartic in a and b does not have rational factors.
What is 2x with the exponent 2 plus 3x plus 1. what is 7n with the exponent 2 plus 9n plus 2. what is 3x with the exponent 2 plus 8x plus 5. what is 7y with the exponent 2 plus 19y plus 10?
The first and third are quadratic expressions in x, the second is a quadratic expressions in n, and the fourth is a quadratic expressions in y. None of them are equations so cannot be solved.
Can a factor pair have an extra addition problem?
Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.Yes and they do in factoring quadratic equations.
How do you solve a quadratic equation that will not factor?
How you solve an equation that doesn't factor is to plug a quadratic equation's format; ax2+bx+c into the quadratic formula which is x=-b+square root to (b2-4ac)/2a.
How an algebric expression with quadratic denominator is solved?
Algebraic expressions can't be solved because they are not equations but they can be simplified.
What expressions appear as a step in solving 3x2 equal x-5 using the quadratic formula?
The following is the answer:
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.
