Factorise $a^{2} - 16n^{2}$.
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 ... show full transcript
Worked Solution & Example Answer:Factorise $a^{2} - 16n^{2}$ - Junior Cycle Mathematics - Question 12 - 2019
Step 1
Factorise $a^{2} - 16n^{2}$
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Answer
The expression can be written as a difference of squares:
a2−(4n)2=(a−4n)(a+4n).
Step 2
Factorise $8x^{2} + 45x - 18$
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Answer
To factor 8x2+45x−18, we first look for two numbers that multiply to 8⋅(−18)=−144 and add to 45. The numbers are 48 and −3.
Thus, we can rewrite the middle term:
8x2+48x−3x−18.
Next, we group the terms:
4x(2x+12)−3(2x+12).
Factoring out the common term:
(2x+12)(4x−3).
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
One possible quadratic expression is:
E(x)=(x+6)(x+1)=x2+7x+6.
Which can be rewritten in the form ax2+bx+c with a=1, b=7, and c=6.
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