Question

✌️Hello✌️

Without actual division, prove that →↓

$2 {x}^{4} - 5 {x}^{3} + 2 {x}^{2} - x + 2 \\ \: is \: divisible \: by \: {x}^{2} - 3x + 2$


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Answer 1

Answer:

Step-by-step explanation:

easy

find factors of x^2-3x+2

x^2-2x-x+2

(x-1)(x-2)

now case 1

x=1

substitute in 2x^4-5x^3+2x^2-x+2

2(1)^4-5(1)^3+2(1)^2-1+2=6-6=0

hence proved but is not complete now case 2

when x=2

2(2)^4-5(2)^3+2(2)^2-2+2=32-40+8=0

hence proved