Question

If x^5+2x^4+X+6is divided by g(X) and the quotient is x^2+5x+7, then the possible degree of g(X) is

Answer 1

x^5 + 2x⁴ + x + 6 is divided by g(x) and the quotient is x² + 5x + 7.

To find : The possible degree of g(x)...

solution : From Euclid division lemma,

a = bq + r , where 0 ≤ r < b

here a = x^5 + 2x⁴ + x + 6 , b = (x² + 5x + 7) and q = g(x)

so, x^5 + 2x⁴ + x + 6 = (x² + 5x + 7)g(x) + r

⇒(x^5 + 2x⁴ + x + 6 - r)/(x² + 5x + 7) = g(x)

from above it is clear that, possible degree of g(x) = highest degree of (x^5 + 2x⁴ + x + 6 - r) - highest degree of (x² + 5x + 7)

= 5 - 2

= 3

Therefore the possible degree of g(x) = 3.

also read similar questions : On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and – 2x + 4, respectively. Fin...

https://brainly.in/question/5482784

on dividing x3-3x2+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.find g(x)

https://brainly.in/question/3135153