By using by using factor theorem show that x+2 is the factor of polynomial 3x^3-x^2-20x-12 hence factorise the given polynomial hence factorise the given polynomial
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Answer:
(x-2) and (x+3) are other two factors
Step-by-step explanation:
Let p(x)=3x³+x²-20x+12,
g(x)=3x-2
It is given that g(x) is factor of p(x).
3x-2)3x³+x²-20x+12(x²+x-6
***** 3x³-2x²
___________________
******** 3x²-20x
******** 3x²-2x
___________________
*********** -18x+12
*********** -18x+12
______________________
Remainder (0)
______________________
BY DIVISION algorithm:
p(x)=g(x)(x²+x-6)
= (3x-2)(x²+3x-2x-6)
= (3x-2)[x(x+3)-2(x+3)]
= (3x-2)(x+3)(x-2)
Therefore,
(x-2) and (x+3) are other two factors of p(x)
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