Question 12 (a) Factorise $a^2 - 16n^2$. (b) One of the factors of $8x^2 + 45x - 18$ is $x + 6$. (i) Factorise $8x^2 + 45x - 18$. (ii) Write down one quadratic expression in $x$, other than $8x^2 + 45x - 18$, that has $x + 6$ as a factor. Give your answer in the form $ax^2 + bx + c$, where $a, b, c \in \mathbb{R}$.

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Question 12 (a) Factorise $a^2 - 16n^2$ - Junior Cycle Mathematics - Question 12 - 2019

Question 12

Question 12 (a) Factorise $a^2 - 16n^2$. (b) One of the factors of $8x^2 + 45x - 18$ is $x + 6$. (i) Factorise $8x^2 + 45x - 18$. (ii) Write down one quadratic ex... show full transcript

Worked Solution & Example Answer:Question 12 (a) Factorise $a^2 - 16n^2$ - Junior Cycle Mathematics - Question 12 - 2019

Step 1

Factorise $a^2 - 16n^2$

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Answer

To factorise the expression $a^2 - 16n^2$ , we recognize it as a difference of squares. This can be expressed as:

$a^2 - (4n)^2 = (a - 4n)(a + 4n)$

Step 2

Factorise $8x^2 + 45x - 18$

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Answer

To factorise $8x^2 + 45x - 18$ , we will find two numbers that multiply to the product of the coefficient of $x^2$ and the constant term, which is $8 \times (-18) = -144$ , while also adding up to the coefficient of $x$ , which is $45$ .

After analyzing factors, we find:

$8x^2 + 48x - 3x - 18$

Now, we can group:

$= 8x(x + 6) - 3(x + 6)$

Factoring out the common term $(x + 6)$ gives us:

$= (8x - 3)(x + 6)$

Step 3

Write down one quadratic expression in $x$, other than $8x^2 + 45x - 18$, that has $x + 6$ as a factor

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Answer

Consider the expression $(x + 6)(x + 1)$ . This expands to:

$x^2 + 7x + 6$

In the required form, we have:

$a = 1, b = 7, c = 6$

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