write the polynomial function f of least degree that had

Find a polynomial of the specified degree that has the given zeros. Degree 4, zeros -2, 0, 2, 4

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

Evaluate $3v^2+5v-6$ for v=1

Factor the following polynomials.
a) ${\displaystyle x^2-6x+9}$
b) ${\displaystyle x^2-25}$
c) ${\displaystyle 3x^2-21x+30}$

Let ${\displaystyle p\left(t\right)=t^5-6t^4+6t^3-6t^2+5t}$.
a) Factorise p(t) as a product of degree 1 polynomials.
b) Give an example of a matrix with characteristic polynomial p(t). That is, find a matrix A such that ${\displaystyle P_a\left(t\right)=p\left(t\right)}$
c) Give an example of a degree 3 polynomial q(t) with real coefficients that has two imaginary roots. For the polynomial q(t) you find, give a matrix that has characterestic polynomial q(t).

Multiply the following polynomials:
${\displaystyle (4x+4)(4x+4)}$

Find the difference of the polynomials.
${\displaystyle (3x^2+2x-1)-(-5x^2+8x+4)}$