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15 (a) Factorise - OCR - GCSE Maths - Question 16 - 2023 - Paper 5

Question 16

15 (a) Factorise. 9x² - 4 (b) Solve by factorisation. 3x² - 2x - 8 = 0 (c) Solve. 2(x - 5) 1 - 3x = 2

Worked Solution & Example Answer:15 (a) Factorise - OCR - GCSE Maths - Question 16 - 2023 - Paper 5

Step 1

Factorise. 9x² - 4

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Answer

The expression is a difference of squares. We can factor it as follows:

$9x^2 - 4 = (3x)^2 - (2)^2 = (3x - 2)(3x + 2)$

Step 2

Solve by factorisation. 3x² - 2x - 8 = 0

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Answer

First, we need to factor the quadratic equation. We look for two numbers that multiply to (3 * -8) = -24 and add to -2. These numbers are -6 and 4.

We can rewrite the equation as:

$3x^2 - 6x + 4x - 8 = 0$

Now, we group the terms:

$3x(x - 2) + 4(x - 2) = 0$

Factoring out the common term gives:

$(3x + 4)(x - 2) = 0$

Setting each factor to zero, we find the solutions:

$3x + 4 = 0 \Rightarrow x = -\frac{4}{3}$
$x - 2 = 0 \Rightarrow x = 2$

Step 3

Solve. 2(x - 5) 1 - 3x = 2

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Answer

Start by simplifying the equation:

$2(x - 5) = 2(1 - 3x)$

Expanding both sides gives:

$2x - 10 = 2 - 6x$

Now, collect all terms involving x on one side and constant terms on the other:

$2x + 6x = 2 + 10$

This simplifies to:

$8x = 12$

Now, solve for x:

$x = \frac{12}{8} = \frac{3}{2}$

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