Question

Using factor theorm, factorize 2x cube - 3x square - 8x - 3

Answer 1

Let p (x) = 2x^3 -3x^2 - 8x -3
All the +ve and -ve values of factors of 3
are 1, -1,3,-3

By taking x as 1
p (1) = 2 (1)^3 - 3 (1)^2 -8 (1)-3
= 2 -3 -8 -3
= -12
So,(x- 1 )is not a factor of p (x)
Again by taking x as -1

p (-1) = 2 (-1)^3 -3 (-1)^2-8 (-1)-3
=-2 -3 +8 -3
= -8+8
=0
So,( x+1 )is a factor of polynomial p (x)
[ As x = -1
= x+1 =0]
For other factors we must try long division method and divide polynomial p (x) by (x +1)
And the quotient after trying long division method would be 2x^2 -5x -3

So the other factor we got is 2x^2 -5x -3


By factorising the other factor
2x^2 -6x+x-3
=2x (x-3) +(x-3)
= (2x+1)(x-3)

Now finally, all the factors of polynomial p (x) we got are (x+1)(2x+1)(x-3)