Question

factorize x^3+4x^2+x-6 using the factor theorem. hence solve the eq. x^3+4x^2+x-6=0

Answer 1

ok, so do u know how to factorise these...?

Answer 2

because its a cubic, it will take the form of
( x + __) (x + __) (x + __)
ok...?

Answer 3

so what time what times what = -6...?
ie what are the factors of 6?

Answer 4

2*3 & 1*6

Answer 5

yep, perfect

Answer 6

so to "prove"which factors to use, simply sub them in to the equation
so start with 2
x^3+4x^2+x-6=0

Answer 7

x^3+4x^2+x-6=0
2^3 + 4(2)^2 + 2 - 6 = 0
8 + 16 + 2 - 6 = 0
20 = 0 so not true, so 2 is not a factor of the eqn

however... if we use -2
x^3+4x^2+x-6=0
-8 + 16 + 2 - 6 = 0
0 = 0 so true, so -2 is a factor

Answer 8

so -2 time what times what = -6?
must be a 3 and a 1, and one of them must be negative (as answer is negative)

Answer 9

can i just have the solution of the answer? :D

Answer 10

so lets assume x = +1
sub into equation
x^3+4x^2+x-6=0
1 + 4 + 1 - 6 = 0
0 = 0 so true, so 1 is a factor

Answer 11

that means that the other factor must be -3

Answer 12

so try the equation
(x - 1) (x + 3) (x + 2)

Answer 13

ok

Answer 14

it's right

Answer 15

sweet, there's ur answer then

Answer 16

ok.. after factoring it.. it asks to solve the eq.