Factorise 2x³-9x²+x+12
Answers
Answer:I hope this helps you
Given,
The cubic equation 2x³-9x²+x+12 is given.
To find,
We have to find the factors of the given cubic equation 2x³-9x²+x+12.
Solution,
The factors of the cubic equation 2x³-9x²+x+12 are (x-4)(2x-3)(x+1).
We can simply find the one root of the cubic equation 2x³-9x²+x+12 by using the hit and trial method.
p(x)= 2x³-9x²+x+12
p(-1) =2(-1)³-9(-1)²+(-1) +12
= -12 +12
= 0
So, (x+1) is one factor of 2x³-9x²+x+12.
By using synthetic division, other factors can be determined,
Depressed equation = 2x²-11x+12
= 2x² - 8x-3x+12
= 2x(x-4)-3(x-4)
= (x-4)(2x-3)
Hence, the factors of 2x³-9x²+x+12 are (x-4)(2x-3)(x+1).