Factorise $n^{2} - 11n + 18$ - Junior Cycle Mathematics - Question 12 - 2017

First, we can rearrange the terms:

$wy + w - y - 1$

Now, we can factor by grouping:

$w(y + 1) - 1(y + 1) = (w - 1)(y + 1)$

First, substitute $x = 4$ into the expression:

$\frac{5}{3(4)^{2}} - \frac{7}{6(4) - 12} = \frac{5}{48} - \frac{7}{24}$

Next, convert $\frac{7}{24}$ to have a common denominator of $48$:

$\frac{7}{24} = \frac{14}{48}$

So, the expression becomes:

$\frac{5}{48} - \frac{14}{48} = \frac{-9}{48} = -\frac{3}{16}$

Recognizing that $4e^{2} - 9$ is a difference of squares, we can factor it as:

$4e^{2} - 9 = (2e)^{2} - 3^{2} = (2e - 3)(2e + 3)$

We are given that the area of the rectangle can be represented as:

$2x^{3} - 13x^{2} + 25x - 12$

Substituting $x - 3$ into the expression:

$x - 3 = 0 \Rightarrow x = 3$

Therefore, the factors are:

$x^{2}(ax^{2} + bx + c) = 2x^{3} - 13x^{2} + 25x - 12$

By polynomial long division, the coefficients yield:

• $a = 2$
• $b = -7$
• $c = 4$