ISAT Grade 11 Algebra. Practice it free.

The greatest common factor of $9x^{2}$ and $6x$ is $3x\textsf{.}$ Factoring gives $3x(3x - 2)$.

More than $2$ means $w > 2$. At most $10$ means $w \le 10$, so $2 < w \le 10$.

$4x^{2} - 81 = (2x)^{2} - 9^{2} = (2x - 9)(2x + 9)$.

Write $50x$ with denominator $h$: $\dfrac{50x}{h} + \dfrac{50xh}{h} = \dfrac{50x + 50xh}{h} = \dfrac{50x(h + 1)}{h}$.

Find two numbers with product $-15$ and sum $2$: $5$ and $-3$. So $x^2 + 2x - 15 = (x+5)(x-3)$.

$x^3 - 27 = (x - 3)(x^2 + 3x + 9) = 0$. The quadratic factor has no real roots, so the only real root is $x = 3$.

The greatest common factor of $12x^{2}$ and $8x$ is $4x$. So $12x^{2} + 8x = 4x(3x + 2)$.

In slope-intercept form $y = mx + b$, the coefficient of $x$ is the slope. Here $m = -5$.