Use factor theorem to factorise 6x^3 + 17x^2 + 4x - 12 completely
Answers
Answer:
f(x)= 6x³+17x²+4x-12.
factors of 12 are +-1;+-2;+-3;+-4;+-6;+-12.
f(-1)= 6×(-1)³+17×(-1)²+4×(-1)-12
= -6+17-4-12
= 17-22
= -5 # 0
hence x+1 is not a factor of f(x)
f(-2)= 6 × (-2)³+17×(-2)²+4×(-2)-12
= -48+68-8-12
= 68-68
= 0
hence x+2 is a factor of f(x).
•°• dividing f(x) by x+2,
x+2|6x³+17x²+4x-12|6x²+5x-6
6x³+12x²
-. -
5x²+4x-12
5x²+10x
-. -
-6x-12
-6x-12
+. +
0
[6×6=36....... LCM of 36 are 1,2,2,3,3.]*
the factors of f(x) are:-
(x+2)(6x²+5x-6). *
(x+2)(6x²+9x-4x-6)
(x+2)[3x(2x+3)-2(2x+3)]
(x+2)(2x+3)(3x-2)
hope it helps
Step-by-step explanation:
(x)= 6x³+17x²+4x-12.
factors of 12 are +-1;+-2;+-3;+-4;+-6;+-12.
f(-1)= 6×(-1)³+17×(-1)²+4×(-1)-12
= -6+17-4-12
= 17-22
= -5 # 0
hence x+1 is not a factor of f(x)
f(-2)= 6 × (-2)³+17×(-2)²+4×(-2)-12
= -48+68-8-12
= 68-68
= 0
hence x+2 is a factor of f(x).
•°• dividing f(x) by x+2,
x+2|6x³+17x²+4x-12|6x²+5x-6
6x³+12x²
5x²+4x-12
5x²+10x
-6x-12
0
HOPE IT IS HELPFUL