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bergausstein
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any hints on how to start this problem?
$12x^4+19x^3-26x^2-61x-28$
$12x^4+19x^3-26x^2-61x-28$
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Is that $12x^2$ perhaps a typo for $12x^4$?bergausstein said:any hints on how to start this problem?
$12x^2+19x^3-26x^2-61x-28$
The roots may not be INTEGERS, as the leading term's coefficient is not 1...Opalg said:Start by looking for integer roots of the polynomial (factors of the constant term). If you find any, then the factor theorem gives you linear divisors of the polynomial.
True, but I like an easy life, so I look for the simplest possible solutions first. (Wink)Deveno said:The roots may not be INTEGERS, as the leading term's coefficient is not 1...
Any hints on how to start this problem?
$\text{Factor: }\:f(x) \:=\:12x^4+19x^3-26x^2-61x-28$
I've never heard of this method and google comes up with nothing. Can you give us a quick run-down?LATEBLOOMER said:i will use dorobostikerlines method.,
$12(x^2-1)^2+19(x^2-1)(x+1)-21(x+1)^2$
i'll let you continue.
Factoring a polynomial means breaking it down into simpler forms, such as multiplying two or more polynomials to get the original polynomial. It is a useful tool in solving equations and understanding the behavior of polynomial functions.
Factoring is important in mathematics because it helps simplify complicated expressions and equations, making them easier to solve. It also allows us to find the roots or zeros of a polynomial, which are important in many applications, such as graphing and optimization problems.
Some tips for factoring polynomials include looking for common factors, using the distributive property, and grouping terms with common variables. It is also helpful to check for special patterns, such as the difference of squares or perfect square trinomials.
A polynomial can be factored if it has more than one term and if it is not a prime polynomial (meaning it cannot be factored further). Additionally, some polynomials may require advanced factoring techniques, such as the quadratic formula or completing the square.
No, factoring can only be used to solve certain types of polynomial equations, such as quadratic equations or equations with special patterns. For more complicated equations, other methods such as the quadratic formula or graphing may be necessary.