Write an equivalent expression by factoring r3 4r2 2r 8 r

Write an equivalent expression by factoring. r^3 - 4r^2 + 2r - 8 r^3 - 4r^2 + 2r - 8 = (Factor completely.)

Solution

given r³-4r²+2r-8

let f(r)=r³-4r²+2r-8

factors of leading coeffient are ±1, factors of constant are ±(1,2,4,8)

possible rational zeroes are ±(1,2,4,8)_/±1

possible rational zeroes are ±(1,2,4,8)

f(-1)=-15,f(1)=-9,f(-2)=-36 ,f(2)=-12, f(-4)=-144 ,f(4)=0 ,f(-8)=-792 ,f(8)=264

so r=4 is zero of given expression . =>(r-4) is the factor

long division:

r-4....].....r³-4r²+2r-8........[r²+2
...............r³-4r²..................
..........................2r-8..........
..........................2r-8..........
.............................0............

=>r³-4r²+2r-8 =(r-4)(r²+2)-------------------------------->answer

=>r³-4r²+2r-8 =(r-4)(r+i2)(r-i2)----------------------->answer