Differentiate $f(x) = x^m(a x+b)^n$.

Differentiate $\displaystyle \frac{ax+b}{cx+d}$.

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$. Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$.

Find their greatest common divisor (GCD) and enter as a normalized polynomial.

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

Find the remainder when dividing two polynomials, by algebraic long division.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

No description given

How to input x^2 and x*y.

No description given

No description given

No description given

Inputting algebraic expressions into Numbas.

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min?