Question

2)
use
factor theorm
to
factorize x3 + 2x² - 5x-6
completly​

Answer 1

Answer:

$(x-2)(x+3)(x+1)$

Step-by-step explanation:

Factors of -6 = $+1,-1,+2,-2,+3,-3,+6,-6$          

[by remainder theorem]                                                              

$p(-1)=(-1)^{3}+(2)(-1)^2-(5) (-1)-6\\:\:\:\:\:\:\:\:\:\:\:\ =>-1+2+5-6\\:\:\:\:\:\:\:\:\:\:\:\ =>0$

∴(x+1) is a factor of x³+2x²-5x-6 [By factor theorem]

on dividing (x+1) with (x³+2x²-5x-6) by long-division method we will get

x²+x-6 as answer

[Sorry I can't send the pic of long-division due to some issues ]

$=>(x^{2} +x-6)(x+1)\\\\=>(x^{2} +3x-2x-6)(x+1)\\\\=>[x(x+3)-2(x+3)](x+1)\\\\=>(x-2)(x+3)(x+1)$

Answer 2

Step-by-step explanation:

put x=2

then x^3+2x^2-5x-6

=(2)^3+2×4-5×2-6

=8+8-10-6

=16-16

=0

now,

x=2 then x-2=0

and x-2 is a factor of this equation

then x^3+2x^2-5x-6 is divided by x-2

and quotient is x^2+4x+3 =0

factorize x^2+(3+1)x+3 =0

x^2+3x+x+3=0

x(x+3) +1(x+3)

(x+3) (x+1) =0

Ans,

and, finally it's factor is (x-2) (x+3) (x+1)

Hope it's help u!!