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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

To factorise the expression, note that it is a difference of squares:

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

Step 2

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

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Answer

First, rewrite the equation:

$3x^2 - 2x - 8 = 0$

To factor, we need to find two numbers that multiply to (3 \times -8 = -24) and add to (-2). These numbers are (4) and (-6):

Rewrite the equation:

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

Now, factor by grouping:

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

This gives:

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

Setting each factor to zero:

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

Step 3

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

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Answer

First, isolate the fraction:

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

Now, expand both sides:

$2x - 10 = 2 - 6x$

Next, combine like terms:

$2x + 6x = 2 + 10 \Rightarrow 8x = 12$

Now, solve for x:

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

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