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<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Factorise $w^{2} - w - 6$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Hence write as a single fraction in its simplest form $\frac{5}{w^{2} - w - 6} + \frac{1}{2w - 6}$.</span></div></li></ol>

Hence write as a single fraction in its simplest form $\frac{5}{w^{2} - w - 6} + \frac{1}{2w - 6}$.

Factorisation of Quadratic Expressions

RSS 2EM EOY P2 2023 Q2b

Quadratic Functions, Equations and Inequalities

<p>Factorise each of the following expressions completely.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$2x^3 - 50x$<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">$6y^2 + 9y - 42$<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">$2ax - 5bx + 15by - 6ay$<span class="inline-marks">[2]</span></div></li></ol>

Factorise each of the following expressions completely.

XMS 2EM WA2 2021 Q6

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Solve the equation $x^2 - 6x - 13 = 3$ with the different methods:</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">by factorisation</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by completing the square</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by the quadratic formula</span><span class="inline-marks">[2]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Solve the equation $-4x^2 + 4x + 3 = 0$ with the different methods:</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">by factorisation</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by completing the square</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">by the quadratic formula</span><span class="inline-marks">[2]</span></div></li></ol></li></ol>

Solve the equation $x^2 - 6x - 13 = 3$ with the different methods:

Solve the equation $-4x^2 + 4x + 3 = 0$ with the different methods:

Solving Quadratic Equations Using the Quadratic Formula

Solving Quadratic Equations by Completing the Square

IP2 Class Test (May 2025) Q3

<p>Factorise each of the following expressions completely.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$-10x^2 - 19x - 6$</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">$18 - 2(a + b)^2$</span><span class="inline-marks">[2]</span></div></li></ol>

Factorisation by Special Identities

IP2 Class Test (May 2025) Q2

<ol class="abc-list"><li><div class="list-item-paragraph">Factorise $6{{x}^{2}}+19x-36$.</div></li><li><div class="list-item-paragraph">Hence, solve $\frac{3x-1}{3x-4}-\frac{13}{6{{x}^{2}}+19x-36}=2$.</div></li></ol>

Rational Equations Reducible to Quadratics

Algebra: Factorising and Using the Result to Solve an Equation

Algebraic Expressions, Identities and Formulae

<p>Factorise $3{{m}^{2}}+2mn-{{n}^{2}}$.</p>

Factorisation of Multivariable Quadratic Expressions

<ol class="abc-list"><li><div class="list-item-paragraph">Factorise $2{{x}^{2}}+13x+15$.</div></li><li><div class="list-item-paragraph">Hence, write down two factors of $21\;315$.</div></li></ol>

Evaluating Expressions using Special Identities

Quadratic Factorisation and Its Applications

<p>Factorise ${{x}^{2}}y-9xy+20y$ fully.</p>

Factorisation of Algebraic Expressions

<p>Factorise $8{{x}^{2}}+14x-4$ completely.</p>

Algebraic Factorisation: Quadratic Forms

<ol class="abc-list"><li><div class="list-item-paragraph">Factorise ${{x}^{2}}+x-6$.</div></li><li><div class="list-item-paragraph">Hence, factorise ${{\left( {{h}^{2}}+1 \right)}^{2}}+\left( {{h}^{2}}+1 \right)-6$ completely.</div></li></ol>

Applying Quadratic Factorisation to Composite Expressions

<p>Factorise completely $10{{x}^{2}}+xy-3{{y}^{2}}$.</p>

Factorise completely $10{{x}^{2}}+xy-3{{y}^{2}}$.

Factorisation of Quadratic Expressions in Two Variables

<p>Factorise $3{{x}^{2}}-30x+72$ completely.</p>

Factorise $3{{x}^{2}}-30x+72$ completely.

Quadratic Expression Factorisation (${ax^2 + bx + c}$)

<p>Factorise $3{{x}^{2}}+19x+20$ completely.</p>

Factorise $3{{x}^{2}}+19x+20$ completely.

Factoring a General Quadratic Trinomial

<p>Factorise $2{{x}^{2}}-10x+8$ completely.</p>

Complete Factorisation of Quadratic Expressions

<p>Factorise $5{{w}^{2}}-23w+12$ completely.</p>

Factorise $5{{w}^{2}}-23w+12$ completely.

Factorisation of Quadratics with Leading Coefficients

<p>Factorise ${{x}^{2}}+9x-36$ completely.</p>

Factoring a Quadratic Trinomial

Quadratic Expression Factorisation

<p>Factorise ${{x}^{2}}-2x-35$ completely.</p>

Quadratic Factorisation

<p>Factorise ${{x}^{2}}-7x+12$ completely.</p>

Factorisation of Quadratics

<ol class="abc-list"><li><div class="list-item-paragraph">Factorise completely ${{p}^{2}}+p-6$.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Hence express $\frac{1}{2-p}+\frac{5p+15}{{{p}^{2}}+p-6}$ as a single fraction in its simplest terms.</div><p style="text-align: right;">[2]</p></li></ol>

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