IGCSE Mathematics 2025 Solving Polynomial Equations.

Welcome to today’s IGCSE Mathematics tutorial. In this lesson, we’ll tackle two high-yield IGCSE math problems — one involving polynomial factorization and the other applying the cosine rule in triangle geometry. These are both frequently tested in IGCSE and essential for exam success.

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You can watch the full class in the video below:

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Question 1: Solve the Equation

x3+x2−4x−4=0x^3 + x^2 – 4x – 4 = 0x3+x2−4x−4=0

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Step-by-Step Solution:

Group the terms for easier factoring: (x3+x2)+(−4x−4)(x^3 + x^2) + (-4x – 4)(x3+x2)+(−4x−4)

Now factor common elements from each group: x2(x+1)−4(x+1)x^2(x + 1) – 4(x + 1)x2(x+1)−4(x+1)

Factor out the common binomial: (x+1)(x2−4)=0(x + 1)(x^2 – 4) = 0(x+1)(x2−4)=0

Now factor the difference of squares: (x+1)(x+2)(x−2)=0(x + 1)(x + 2)(x – 2) = 0(x+1)(x+2)(x−2)=0

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Final Answer:

The solutions are: x=−1,x=−2,x=2x = -1,\quad x = -2,\quad x = 2x=−1,x=−2,x=2

Roots of the equation: −2, −1, 2\boxed{-2,\ -1,\ 2}−2, −1, 2​

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Question 2: Using the Cosine Rule in Triangle ABC

Given:

• Side AB=8 cmAB = 8\, \text{cm}AB=8cm
• Side AC=6 cmAC = 6\, \text{cm}AC=6cm
• Angle ∠A=60∘\angle A = 60^\circ∠A=60∘
• Find side BCBCBC

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Applying the Cosine Rule:

The cosine rule is given by: a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 – 2bc\cos Aa2=b2+c2−2bccosA

Where:

• a=BCa = BCa=BC (unknown)
• b=AC=6 cmb = AC = 6\, \text{cm}b=AC=6cm
• c=AB=8 cmc = AB = 8\, \text{cm}c=AB=8cm
• ∠A=60∘\angle A = 60^\circ∠A=60∘

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Plug in the values:

a2=62+82−2⋅6⋅8⋅cos⁡(60∘)a^2 = 6^2 + 8^2 – 2 \cdot 6 \cdot 8 \cdot \cos(60^\circ)a2=62+82−2⋅6⋅8⋅cos(60∘) a2=36+64−96⋅0.5a^2 = 36 + 64 – 96 \cdot 0.5a2=36+64−96⋅0.5 a2=100−48=52a^2 = 100 – 48 = 52a2=100−48=52

Now take the square root: a=52=4⋅13=213a = \sqrt{52} = \sqrt{4 \cdot 13} = 2\sqrt{13}a=52​=4⋅13​=213​

Final Answer: BC=213 cm≈7.21 cmBC = \boxed{2\sqrt{13}\ \text{cm}} \approx 7.21\, \text{cm}BC=213​ cm​≈7.21cm

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Watch more educational videos and past questions: https://youtube.com/@allcbts

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Why These Topics Are Crucial for IGCSE 2025

• Polynomial factorization helps in solving cubic equations, essential in algebra.
• Cosine Rule is a vital part of non-right triangle problems, often tested in Paper 2 and 4.

By mastering these skills, you increase your chance of scoring full marks in structured and objective questions.

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Solve IGCSE Mathematics 2025 questions on polynomials and triangle geometry using this step-by-step guide. Learn factorization and cosine rule applications for exam success.

Keywords:
IGCSE Maths 2025, solve x^3 + x^2 – 4x – 4, cosine rule IGCSE, triangle side calculation, IGCSE polynomial factorization, Cambridge exam math