Question

Factorise 10x² - 18x³+ 14x⁴

Answer 1

`10x^2 = 2 xx 5 xx x xx x`
`18x^3 = 2 xx 3 xx 3 xx x xx x xx x`

`14x^4 = 2 xx 7 xx x xx x xx x xx x`

The common factors of the three terms are 2, x and x.

Therefore,

10x² - 18x³ + 14x⁴

`= (2 xx x xx x xx 5) – (2 xx x xx x xx 3 xx 3 xx x) + (2 xx x xx x xx 7 xx x xx x)`

`= 2 xx x xx x xx[(5 – (3 xx 3 xx x) + (7 xx x xx x)]`  .... (combining the three terms) 

`=2x^2 xx (5 –  9x + 7x^2)`

`=2x^2 xx (7x^2 - 9x + 5)`.