MASH Bath: Question Bank

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Finding the product of a linear function of the form $mx+c$ and a cubic function of the form $ax^3+bx^2+cx+d$.

Finding the product of two linear functions of the form $mx+c$ and a quadratic function of the form $ax^2+bx+c$.

Finding the product of three linear functions of the form $mx+c$.

Finding the product of two linear functions of the form $mx+c$.

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculating a quartic polynomial by squaring a quadratic expression of the form $ax^2+bx+c$.

Multiplying a linear expression of the form $mx+c$ by a quadratic expression of the form $ax^2+bx+c$. 

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Factorising a quadratic expression of the form $ax^2+bx+c$, where $a>1$.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{x+a}$ as partial fractions in the form $\frac{A}{x+a}+Bx+C$.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+C$.

Rewrite the expression $\frac{mx+a}{nx+b}$ as partial fractions in the form $A+\frac{B}{nx+b}$.

Rewrite the expression $\frac{x+a}{x+b}$ as partial fractions in the form $A+\frac{B}{x+b}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{n}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{cx+d}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{n}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.