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Can all quadratic equations be solved?
Well, that depends on what you mean "solve by factoring." For any quadratic equation, it is possible to factor the quadratic, and then the roots can be recovered from the factors. So in the very weak sense that every quadratic can be solved by a method that involves getting the factors and recovering the roots from them, all quadratic equations can be solved by factoring. However, in most cases, the only way of factoring the quadratic in the first place is to first find out what its roots are, and then use the roots to factor the quadratic (any quadratic polynomial can be factored as k(x - r)(x - s), where k is the leading coefficient of the polynomial and r and s are its two roots), in which case trying to recover the roots from the factors is redundant (since you had to know what the roots were to get the factors in the first place). So to really count as solving by factoring, it makes sense to require that the solution method obtains the factors by means that _don't_ require already knowing the roots of the polynomial. And in this sense, most quadratic equations are not solvable through factoring.
What is the meaning degree of polynomial?
The degree of a polynomial is the highest exponent on any independent variable in the polynomial.
What are the roots of polynomial?
The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.
How would you use special factoring patterns to factor a given polynomial?
One example is the special pattern known as difference of squares. For any a and b we have a2-b2= (a-b)(a+b) We can do similar things with sums and differences of cubes when the patten tells us how to factor the polynomial. So if we have 16x2-4=(4x)2-22=(4x-2)(4x+2) using the pattern.
What is the answer to the question 'what is factoring'?
Factoring is breaking down an expression into two or more simpler expressions. When you are factoring, you must simply the numbers and variables until they cannot be broken down any further.
