the factored form of the polynomial is:
p(x) = x*(x - 6)*(x + 4)
And the standard form is:
p(x) = x^3 - 2x^2 - 24x
If we know that a polynomial of degree N has the zeros x₁, x₂, ..., xₙ, then we can write that polynomial as:
p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
Where a is the leading coefficient, in this case, we can assume it is 1.
That is the factored form of the polynomial.
In this case, we know that the zeros are 0, 6 and -4, so our polynomial is:
p(x) = (x - 0)*(x - 6)*(x + 4) = x*(x - 6)*(x + 4)
To get it in standard form, we just extend the above product:
p(x) = x*(x - 6)*(x + 4) = (x^2 - 6x)*(x + 4) = x^3 + 4x^2 - 6x^2 - 24x
p(x) = x^3 - 2x^2 - 24x
Concluding, the factored form of the polynomial is:
p(x) = x*(x - 6)*(x + 4)
And the standard form is:
p(x) = x^3 - 2x^2 - 24x
If you want to learn more about polynomials:
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