Question

find the remainder using remainder theorem x⁴+ x³-2x ²+ x+1 divided by x-2​

Answer 1

Answer:

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Step-by-step explanation:

X-2=0

X=2

Now

P(2)= 2^3-2(2)^2+2+1

= 8-8+3

=3

Answer 2

Use Remainder Theorem.

If a polynomial p(x) is divided by (x - a), then remainder is given by p(a).

If remainder is zero, then (x - a) is a factor of p(x).

p(x) = x⁴ - x³ + 2

Rewrite the divisor as 2(x - (-5/2))

Now Rem|p(x)/(2x + 5)|

= ½((-5/2)⁴ - (-5/2)³ + 2)

= ½(625/16 + 125/8 + 2)

= ½(625/16 + 250/16 + 32/16)

= ½(907/16) = 907/32

=> Final Remainder = 2 x 907/32 = 907/16

:-)