8x3 + 12x2 - 44x - 24
= 4(2x3 + 3x2 - 11x - 6)
= 4(2x3 - 4x2 + 7x2 - 14x + 3x - 6)
= 4[2x2(x - 2) + 7x(x - 2) + 3(x - 2)]
= 4(x - 2)(2x2 + 7x + 3)
= 4(x - 2)(2x2 + 6x + x + 3)
= 4(x - 2)[2x(x + 3) + 1(x + 3)]
= 4(x - 2)(x + 3)(2x + 1)
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this term 2x is not a polynomial. this term is a monomial. since only one term was listed it can not be a polynomial. A polynomial is like four or more terms. a trinomial is three terms and a binomial is two terms.
2x is just 2x and it is not a polynomial. This is a monomial because it just has one term. a polynomial is four or more terms.
Yes, it can be considered a polynomial with one term.
The degree of a polynomial is the highest exponent in the polynomial.
If you have the zeros of a polynomial, it is easy, almost trivial, to find an expression with those zeros. I am not sure I understood the question correctly, but let's assume you have the zero 2 with multiplicity 2, and other zeros at 3 and 5. Just write the expression: (x-2)(x-2)(x-3)(x-5). (Example with a negative zero: if there is a zero at "-5", the factor becomes (x- -5) = (x + 5).) You can multiply this out to get the polynomial if you like. For example, if you multiply every term in the first factor with every term in the second factor, you get x2 -2x -2x + 4 = x2 -4x + 4. Next, multiply each term of this polynomial with each term of the next factor, etc.