A function which renders the factorisation of a number in LaTeX.

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Cofactors Determinant and inverse of a 3x3 matrix.

Cofactors Determinant and inverse of a 3x3 matrix.

Another transposition question, which requires (basic) factorisation.

rebelmaths

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

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Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

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Quadratic factorisation that does not rely upon pattern matching.

Cofactors Determinant and inverse of a 3x3 matrix.

Cofactors Determinant and inverse of a 3x3 matrix.

Given polynomial $f(X)$, $g(X)$ over $\mathbb{Q}$, find polynomials $q(X)$ and $r(X)$ over $\mathbb{Q}$ such that $f(X)=q(X)g(X)+r(X)$ and $\operatorname{deg}r(X) \lt \operatorname{deg}g(X)$.

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Factorise 4 polynomials over $\mathbb{Z}_5$.

$f(X)$ 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.