Consider the polynomial P(x)=4+7(x-5)+2(x-5)^3

MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider the polynomial

P(x)=4+7(x-5)+2(x-5)^3.

Which statement correctly identifies the degree of

P

and justifies that choice? (a)

P

is fourth degree because the exponents of

(x-5)^3

and

(x-5)

add to give

4

.},{ (b)

P

is third degree because the highest non-zero power of

(x-5)

present is

3

. (c)

P

is second degree since the

x^3

term produced by

(x-5)^3

cancels out when expanded and combined. (d) The degree of

P

cannot be determined until all terms are expanded and simplified.