Question

without actual division prove that 2 x 4 - 5 x cube + 2 x square minus x + 2 is divisible by x cube minus 3 X + 2​

Answer 1

Answer:

first

x^2-3x+2

x^2-2x-x+2

x(x-2)-1(x-2)

so,(x-2)and(x-1) are factor

# for first factor

(x-2)

x-2=0

x=2

p(x)=2x^4-5x^3+2x^2-x+2

=2(2)^4-5(2)^3+2(2)^2-2+2

=40-40

=0

so (x-2) is factor

# for second factor

(x-1)

x-1=0

x=1

p(x)=2x^4-5x^3+2x^2-x+2

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

=6-6

=0

hence (x-1) is a factor

so both (x-2) and (x-1) are factor of given polynomial

Hope so it helps you

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