The shape is twice the size of the original, scale factor 2; the scale factor is -2 because it is inverted and is on the opposite side of the expansion center Answer: Expansion, scale factor -2, center of expansion (1, 5) Figure X is maped to Y with scale factor -0 5, and expansion center (5, 5)

(b) Use your answers to (a) to find all the roots of (i) x 3 ? 3x 2 ? 6 x + 8 = 0 (ii) x3 + 8x2 + 12 x ? 9 = 0 (iii) 2 x 3 ? x 2 ? 117 x ? 324 = 0 2 Explain how you know that (a) (x ? 3) is a factor of x 3 ? 2 x 2 + x ? 12 (b) (x + 5) is a factor of 2 x 3 + 6 x 2 ? 23x ? 15 (c) (2 x ? 1) is a factor of

(x?1) is a factor of f x( ) when f x( ) is divided by (x+1) the remainder is 8 b) Hence solve the equation f x( ) = 0 C2H , p = ? 2 , q = ? 5 , x = ?1, 2, 3 Question 24 (***) f x x x x( ) ? ? ? +2 7 2 13 2 a) Use the factor theorem to show that (2 1x+) is a factor of f x( ) b) Find the exact solutions of the equation f x

Basic Algebra (Answers) Answer outline and marking scheme for question: 1 Give yourself marks for mentioning any of the points below: a) Use the factor theorem f (-2) = -64 + 72 - 6 - 2 = 0, thus (x+2) is a factor f (1/4) = 1/8 + 9/8 + 3/4 - 2 = 0, thus (4x-1) is a factor (2 marks) b) (i) replacing the given equation with its factors:

4 Factorise fully the following polynomials You may need to use the factor theorem: (a) x3 + 2x2 + x [2] (b) x3 26x + 11x 6 [3] (c) x3 4x2 + 5x 2 [3] (d)2x3 + 7x2 + 2x 3 [3] (e) x4 2x2 + 1 [2] 5 Solve the following equations Hint: to save time, use your answers from the previous question: (a) x3 + 2x2 + x = 0 [2] (b) x3 6x2 + 11x 6 = 0

• Use the Corbett maths videos to recall the facts and skills • Use the corresponding textbook exercises to secure your understanding and develop fluency o Do the workout section to rehearse the basic skills o Do the apply section to improve your reasoning, problem solving and application of skills Dr Frost:

Factor Theorem Corbettmaths Ensure you have: Pencil or pen, a calculator Guidance 1 Read each question carefully before you begin answering it 2

Read each question carefully before you begin answering it 2 Check your answers seem right 3 Always show your workings Revision for this topic

Further Maths Revision Notes Complete Revision Notes 1 - This document is more user friendly and doesn't go into so much detail as the second one

Read each question carefully before you begin answering it 2 Check your answers seem right 5 Always show www corbettmaths com/contents OR Circle Theorems 64, 65 The Highest Common Factor (HCF) of two numbers is 6

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