Question

Factorise:

(1) x² − 2x − 99
(2) 3p² − 10p − 25
(3) 125x³ − 216y³
(4) 128 + 2x³

Answer 1

(1) The factors of x² − 2x − 99 are:
$$\begin{gathered} =x^2-2x-99 \\ =x^2-11x+9x-99 \\ =x\left(x-11\right)+9\left(x-11\right) \\ =\left(x-11\right)\left(x+9\right) \end{gathered}$$

(2) The factors of 3p² − 10p − 25 are:
$$\begin{gathered} =3p^2-10p-25 \\ =3p^2-15p+5p-25 \\ =3p\left(p-5\right)+5\left(p-5\right) \\ =\left(3p+5\right)\left(p-5\right) \end{gathered}$$

(3) The factors of 125x³ − 216y³ are:
$$\begin{gathered} =125x^3-216y^3 \\ ={\left(5x\right)}^3-{\left(6y\right)}^3 \\ =\left(5x-6y\right)\left(25x^2+30xy+36y^2\right) \end{gathered}$$

(4) The factors of 128 + 2x³ are:
$$\begin{gathered} =128+2x^3 \\ =2\left(64+x^3\right) \\ =2\left[{\left(4\right)}^3+{\left(x\right)}^3\right] \\ =2\left(4+x\right)\left(16+x^2-4x\right) \end{gathered}$$