Question

Using remainder Theorem, factorise:

2x³ + 7x² − 8x – 28 Completely

Answer 1

Let f (x) = 2x³ + 7x² − 8x − 28
For x = 2,
f(x) = f(2) = 2(2)³ + 7(2)² − 8(2) − 28 = 16 + 28 − 16 − 28 = 0
Hence, (x − 2) is a factor of f(x).

∴ `2x^3 +  7x^2 - 8x - 28 =( x - 2)( 2x^2 + 11x + 14)`
 = `(x- 2) ( 2x^2 + 4x + 7x  + 14)`
= (x - 2) [ 2x (x + 2)+ 7( x+ 2)]
= (x -2) (x +2)( 2x + 7)